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Introduction 

Virginia Woolf, an English novelist, gained widespread attention in the 20th century. Her novels garnered the most acclaim, despite the fact that she also produced nonfiction, biography, letters, and diaries. Her works are under the modernist literary movement that was popular between the two world wars. Woolf’s writing style, known as stream of consciousness, is a literary technique that uses a character’s continuous internal monologue to create a more lifelike portrait of that character.

Life

Virgina Woolf was born in 1882. Woolf’s writing reflects the quickly developing society in which she lived and worked, including its shifting gender, sexuality, and socioeconomic norms. Woolf was educated at home, with unrestricted access to her father’s extensive library.

Woolf’s first of many mental breakdowns began after her mother’s death in 1895. Her half-sister Stella took charge of the home when she was thirteen years older than Woolf, and Vanessa took over the reins two years later. After Leslie Stephen’s death in 1904 and a subsequent mental breakdown, Woolf attempted suicide.

While she was recuperating, her sister Vanessa moved the family to London’s trendy Bloomsbury neighbourhood. There, Woolf began publishing her works at the Thursday night gatherings with Thoby’s Cambridge friends, which became the germ for the Bloomsbury Group.

At this period, Stephen and his four siblings travelled to Paris and Italy in 1904, and then to Greece two years later, when typhoid fever hit Woolf and Thoby, ultimately claiming Thoby’s life.

In 1912, Woolf married Leonard Woolf, a member of the Bloomsbury group and a recent returnee after seven years of duty in the Ceylonese civil service. Not long after, she attempted suicide again, and the next three years were marked by extreme emotional pain. At this time, Woolf wrote and published her first novel, The Journey Out, in 1915.

Virginia Woolf

Two years later, in the basement of their house, the Woolfs founded their own publishing house, the Hogarth Press, which went on to print works by Sigmund Freud, T. S. Eliot, Katherine Mansfield and other authors in addition to Woolf’s.

Desmond MacCarthy, a Bloomsbury Group member writing as “Affable Hawk,” and Virginia Woolf argued about women’s intellectual capacities in 1920s letters written to the New Statesman’s editor.

Woolf continued to write and publish during the 1930s and 1920s, creating a number of further books and articles. In 1941, Woolf self-immolated in the River Ouse  after stuffing her pockets full of rocks out of anxiety that she was about to experience another mental breakdown.

Works

The city, time, the subconscious, perception, and the impacts of war are only few of the primary topics explored by Woolf in her writing. Woolf is known for her novels, particularly Mrs. Dalloway, but she also wrote a number of short stories.

Virginia had begun her first novel a number of years before she married Leonard. The piece was first published under the title Melymbrosia. After nine years and many draughts, 1915 saw the publication of The Journey Out.

To the Lighthouse, another critical darling, was acclaimed for its innovative first-person point of view.

Set against the beautiful backdrop of the Scottish Island of Skye, this modernist classic delves deep into the complexities of human connection.

Woolf found in Sackville-West the inspiration for Orlando, her 1928 novel about an English nobleman who mysteriously changes into a woman at the age of 30, and who then outlives three centuries of English history.

Based on her lectures at women’s institutes, Woolf published the feminist essay A Room of One’s Own in 1929.

The Waves (1931), a play-poem constructed in the six voices of distinct characters, was Woolf’s next work that pushed the boundaries of the narrative.

Virginia Woolf’s final work was The Years, a multi-generational family saga.

The next year saw the publication of the essay Three Guineas, which continued the feminism and environmentalism of A Room of One’s Own while also tackling Nazism and war.

She won widespread acclaim for her ability to seamlessly incorporate surreal elements into otherwise high-stakes narratives.

Conclusion

Virginia Woolf used the “stream of consciousness” technique to convey both the montage-like a memory’s impression and the inner lives of her characters. Woolf’s “stream of consciousness” style is a literary approach that employs a character’s continual internal monologue to paint a more realistic picture of that person.

Frequently Asked Questions 

1. What was Virginia Woolf’s outlook on life?

Ans. Virginia Woolf believed that life was full of beauty and joy, but also full of pain and sorrow. She believed that life was a complex and ever-changing experience, and that it was important to embrace both the good and the bad. She also believed that life was a journey, and that it was important to take risks and explore new ideas and experiences.

2. What social impact did Virginia Woolf have?

Ans. Her works, particularly To the Lighthouse and Mrs. Dalloway (1925), are what made her most famous (1927). She also published groundbreaking studies on literary theory, women’s writing, power politics, and artistic philosophy.

3. What influenced Virginia Woolf’s views on men?

Ans. Virginia was influenced by feminism as an adolescent. The close relationship she had with her parents—the beautiful wife of accomplished and distinguished Leslie Stephen and he himself—had a major impact on Virginia’s perspective on men. She was consistently there for him, ready to listen and cheer him on.

Introduction 

On July 21, 1899, Ernest Hemingway was born in Oak Park, Illinois, an affluent Chicago neighbourhood where the American architect Frank Lloyd Wright resided.

Father of Ernest Hemingway, Dr. Clarence E. Hemingway, and his mother, a devout Christian who had abandoned a rich singing career, raised their six children, of which Ernest was the third and eldest male. Hemingway’s body of work is vast, and his unique style continues to serve as an influence for contemporary authors. His attitude and never-ending search for adventure were as significant as his artistic skill.

Biography 

The Nobel Prize-winning author Ernest Hemingway is recognised as one of the finest American authors of the twentieth century. Although Clarence and Grace Hemingway raised their son in this conventional Chicago neighbourhood, they also maintained a cottage in Northern Michigan, where they travelled frequently.

Hemingway wrote to the high school publication Trapeze and Tabula, focusing mostly on sports journalism throughout his tenure there.

The aspiring journalist began working for the Kansas City Star immediately after graduating from college. Prior to serving his country as an ambulance driver in World War I and heading to the Italian front, where he was wounded in 1918, he worked for the Kansas City Star, gaining valuable experience that later shaped his straightforward writing style.

In 1927, Hemingway divorced Hadley Richardson and afterwards married Pauline Pfeiffer. They split immediately upon Hemingway’s return from the Spanish Civil War, where he had served as a journalist, since this marriage was also bound to fail.

Martha Gellhorn, who would become his third wife, was wed to him in 1940. During World War Two, he separated from her after meeting Mary Welsh in London.

When one of his masterpieces, “The Old Man and the Sea” , was released in 1952,Hemingway travelled to Africa on safari, but two subsequent plane crashes nearly cost him his life, leaving him in pain or in poor health much of the remaining years of his life.

Throughout the 1930s and 1940s, Hemingway lived permanently in Florida, Cuba and Key West. Nevertheless, he relocated to Ketchum, Idaho, from Cuba in 1959, eventually, in the 1961’s summer, he passed away.

Hemingway’s characters unmistakably represent his own morals and outlook on life. Hemingway left a sizable body of writing behind, some of which have been published.

Style

Maybe the 20th century’s most widely imitated writer, Hemingway’s literary style was also the most recognisable.

He was on a mission to rid his own work of unnecessary jargon, flowery language, and excess description.

Earnest Hemingway

Hemingway invented the technique of presenting a series of acts by utilising short, straightforward phrases from which all commentary or emotive hyperbole has been omitted in an attempt to be as unbiased and truthful as possible. 

.The result is short, tightly focused prose that is straightforward and emotionless, but frequently evocative and able to subtly communicate considerable irony.Similar to his writing style, Hemingway’s conversation was straightforward, natural-sounding, and original. Especially between the 1930s and the 1950s, this aesthetic was felt everywhere novels were written.

Works

Hemingway published his first book of fiction, “Three Tales and Ten Poems,” in 1923. Short stories were the ones that got a blossoming talent noticed, whereas poetry were ignored.

Hemingway depicts the early years of Nick Adam’s life in “Within Our Time,” published in 1925, as a world of sorrow and violence by drawing on incidents from his own life at the University of Michigan.

When “The Sun Also Rises” was out in May of 1926, it was Hemingway’s second novel. The “lost generations” are the primary characters in this book, and they represent a group of Americans and Britons who have been physically and psychologically scarred by the war.

Hemingway’s “A Farewell to Arms” came out in December 1929. The idea of man’s helplessness in the face of the brutality of war is beautifully rendered in Hemingway’s classic work.

In 1932, Ernest Hemingway published his nonfiction work Death in the Afternoon.

Hemingway’s “For Whom the Bell Tolls” is widely considered to be his masterpiece, yet after its publication, he didn’t write another novel for ten years.

Hemingway’s novella “The Old Man and the Sea” first out in 1952. The novella was immediately heralded as a masterpiece.

After his death, several of his works were published. It is generally agreed that he is among the most significant American authors of the 20th century.

Conclusion 

Even though Hemingway was famous before he was even middle-aged, reputable critics continue to support his popularity. The majority of the impact of these phrases comes from repetition and rhythm; they are mostly made up of nouns and verbs, contain few adverbs and adjectives, and are largely devoid of these words

Frequently Asked Questions

1. What was the effect of Ernest Hemingway earning nobel prize?

Ans. With his tough but frail masculinity, which contributed to a myth that imprisoned the writer and frightened the post-World War II generation, and his deceptively simple, spare prose that was full of implied meaning, Ernest Hemingway was awarded the 1954 Nobel Prize in Literature and had a significant influence on other authors.

2. In what ways do you think Hemingway’s work exemplifies a new kind of fiction?

Ans. His approach to writing was novel to an extent. By cutting out unnecessary words and phrases, he could reduce a paragraph or sentence to its barest necessities. There, he came up with a new way of writing dialogue and descriptions that cut right to the story’s meat.

3. How did Hemingway’s writing represent a novel form of fiction?

Ans. His writing style was a little bit groundbreaking. A paragraph or sentence was pared down to its minimal essentials by him by removing whatever he didn’t need. There, he was able to invent a fresh method for writing descriptions and dialogue that quickly got to the point of the narrative.

Introduction

A quadrilateral that can be completely inscribed in a circle is called a cyclic or inscribed quadrilateral and conversely, a circle passing through all four vertices of a quadrilateral is known as a circumcircle. The centre of such a circle is called the circumcentre and the radius is known as the circumradius. Another way of saying that a quadrilateral is cyclic is to say that its vertices are concyclic. Interestingly, while you can inscribe all triangles into a circle, the same is not possible with all quadrilaterals and instead, only some of them can be cyclic.

Definition – What is cyclic quadrilateral

A quadrilateral with all its vertices lying on a circle is called a cyclic quadrilateral. However, not every quadrilateral can be inscribed in a circle and thus, the quadrilateral must be cyclic by design.

The figure below shows a cyclic quadrilateral EFGH inscribed inside a circle. Its sides are represented by e, f, g, and h, and the diagonals are represented by p and q. Note that the diagonals need not be of equal length.

A cyclic quadrilateral

Angles

Angles opposite to each other inside a cyclic quadrilateral sum up to 180⁰, i.e., they are supplementary. For instance, in the figure shown above, we have a cyclic quadrilateral EFGH. If the angles made at the vertices of this quadrilateral are represented by ∠E, ∠F, ∠G, and ∠H, respectively, then we can write the following:

\(\angle E + \angle G = {180^0}\)

\(\angle F + \angle H = {180^0}\)

Further, just like all other quadrilaterals, the sum of all the angles of a quadrilateral is equal to 360⁰ and this can be easily proven by adding the two equations written above.

Radius

There are a few other interesting properties related to the side lengths of a cyclic quadrilateral. Given the cyclic quadrilateral EFGH as above, we can write the following:

semi perimeter of circumcircle, s = \(\frac{{e + f + g + h}}{2}\)

Radius of circumcircle\(r = \frac{1}{4} \times \sqrt {\frac{{(eg + fh) \times (eg + fh) \times (eh + fg)}}{{(s – e) \times (s – f) \times (s – g) \times (s – h)}}} \)

Diagonals

Once again, we look at the cyclic quadrilateral we saw above, with diagonals represented by p and q. Another interesting property that emerges is between the side lengths and diagonals of such a quadrilateral. We can write the following:

length of diagonal p \( = \frac{{(eg + fh) + (eh + fg)}}{{(ef + gh)}}\)

length of diagonal q \( = \frac{{(eg + fh) + (ef + gh)}}{{(eh + fg)}}\)

Area

We can also examine properties related to the area of cyclic quadrilaterals. Looking at the figure shown before, if we have the semi perimeter given by s, we can write the following:

semi perimeter s \( = \frac{{e + f + g + h}}{2}\)

Area \( = \sqrt {(s – e) \times (s – f) \times (s – g) \times (s – h)} \)

Theorems

Ptolemy’s theorem: This is an interesting theorem related to cyclic quadrilaterals. Let us discuss and prove it. As before, we have a cyclic quadrilateral represented by EFGH. Using Ptolemy’s theorem, which states that in cyclic quadrilateral, the product of the diagonals equals the sum of the products of pairs of two opposite sides. That is,

\((EF \times GH) + (EH \times FG) = EG \times FH\)

Or,

\({\bf{eg}} + {\bf{fh}} = {\bf{pq}}\)

This can be proven as follows. We take a cyclic quadrilateral ABCD and suppose that K is the point where its diagonals intersect. This is shown in the figure below.

Ptolemy’s theorem

Since the angle subtended by a chord are the same at any point on the circle, we can write for chord AD, chord BC, and chord AB,

∠ABD =∠ACD

∠BCA =∠BDA

∠BAC =∠BDC

Ptolemy’s theorem

Next, we take a point E on the diagonal AC such that ∠EBC = ∠ABD. From the previous three equations, we already have ∠BCA =∠BDA and thus, we have two similar triangles, namely, triangle EBC and triangle ABD. Thus, we can write the following:

\(\begin{array}{l}\frac{{CB}}{{DB}} = \frac{{CE}}{{AD}}\\CB \times AD = CE \times DB\end{array}\)

Let us consider this equation 1 and add ∠KBE on both sides of the equation. We then get

\(\begin{array}{*{20}{c}}{\angle {\bf{EBC}}{\rm{ }} + \angle {\bf{KBE}}{\rm{ }} = \angle {\bf{ABD}}{\rm{ }} + \angle {\bf{KBE}}}\\{\angle {\bf{KBC}}{\rm{ }} = \angle {\bf{ABE}}}\end{array}\)

Ptolemy’s theorem

Similarly, we can find similar triangles BDC and ABE and do something similar, leading us to the following relations:

\(\begin{array}{l}\frac{{AB}}{{BD}} = \frac{{AE}}{{DC}}\\DC \times AB = AE \times BD\end{array}\)

We call this equation 2 and add it to equation 1 to get

\(\begin{array}{l}CB \times AD + DC \times AB = CE \times DB + AE \times BD\\CB \times AD + DC \times AB = (CE + AE) \times BD\\CB \times AD + DC \times AB = AC \times BD\end{array}\)

And thus, we have our proof.

Properties

Let’s discuss some properties regarding cyclic quadrilateral:

1. We have discussed that the opposite angles of a cyclic quadrilateral are supplementary. This is always true and thus, if the sum of opposite angles of a quadrilateral is 180⁰, then the quadrilateral is necessarily cyclic.
2. A rhombus can never be a cyclic quadrilateral since its opposite angles do not sum up to 180⁰.
3. Given a cyclic quadrilateral EFGH, with side lengths e, f, g, and h respectively, with diagonals p and q, let the diagonals intersect at a point I. We can write

\(EI \times IG = FI \times IH\)

1. Joining the midpoints of the sides of a quadrilateral gives us a parallelogram.
2. The perpendicular bisectors of the sides of a cyclic quadrilateral meet at the centre and are concurrent.

Problems and Solutions

1. In a cyclic quadrilateral EFGH, \({\bf{if}}{\rm{ }}\angle {\bf{E}}{\rm{ }} = {\rm{ }}{\bf{8}}{{\bf{5}}^{\bf{0}}},{\rm{ }}{\bf{find}}{\rm{ }}\angle {\bf{G}}\)

Since the opposite angles of a cyclic quadrilateral are supplementary, we can write

\(\begin{array}{*{20}{c}}{\angle {\bf{E}}{\rm{ }} + {\rm{ }}\angle {\bf{G}}{\rm{ }} = {\rm{ }}{\bf{18}}{{\bf{0}}^{\bf{0}}}}\\{\angle {\bf{G}}{\rm{ }} = {\rm{ }}{\bf{18}}{{\bf{0}}^{\bf{0}}}–{\rm{ }}{\bf{8}}{{\bf{5}}^{\bf{0}}} = {\rm{ }}{\bf{9}}{{\bf{5}}^{\bf{0}}}}\end{array}\)

2. Let the side lengths e, f, g, and h of a cyclic quadrilateral be 3, 6, 4, and 7m respectively. What is its area?

For a cyclic quadrilateral, the semi perimeter is given by

\(s = \frac{{e + f + g + h}}{2}\)

And the area is given by

\(A = \sqrt {(s – e) \times (s – f) \times (s – g) \times (s – h)} \)

On substituting the values, we get s = 10 m. And therefore, the area is

\(\begin{array}{l}A = \sqrt {(10 – 3)(10 – 6)(10 – 4)(10 – 7)} \\A = \sqrt {7 \times 4 \times 6 \times 3} \\A = \sqrt {504} {m^2}\end{array}\)

3. Let the side lengths of a cyclic quadrilateral be 2, 5, 3, and 6m. Find the product of the diagonals.

We can use Ptolemy’s theorem to solve this problem. We know that

\(\begin{array}{l}EF \times GH + EH \times FG = EG \times FH\\EG \times FH = 2 \times 3 + 5 \times 6 = 36\end{array}\)

Summary

This article discussed what cyclic quadrilaterals are by explaining their definition and listed a few properties related to the sides, angles, the circumcircle, the diagonals, and the area of a cyclic quadrilateral. Further, we looked at a few theorems related to such quadrilaterals, namely, Ptolemy’s theorem.

Enhance your understanding of Cyclic Quadrilaterals by enrolling in our Class 9 Maths Tuitions.

Frequently Asked Questions

1. Is every square a cyclic quadrilateral?

Yes. The sum of the opposite angles inside a square always add up to 180⁰ and therefore, all squares are cyclic in nature.

2. If we are given the lengths of sides of a cyclic quadrilateral, how do we find its diagonals?

Such problems can be solved using the properties of cyclic quadrilaterals. The diagonals p and q of a cyclic quadrilateral EFGH can be obtained via the formulae given below:

length of diagonal p \( = \sqrt {\frac{{(eg + fh) + (eh + fg)}}{{(ef + gh)}}} \)

length of diagonal q \( = \sqrt {\frac{{(eg + fh) + (ef + gh)}}{{(eh + fg)}}} \)

3. Are all parallelograms cyclic quadrilaterals?

Not necessarily. The opposite angles inside a parallelogram aren’t always supplementary and thus, may not add up to 180⁰ , which means that only some parallelograms can be cyclic.

4. How can we prove that the opposite angles of a cyclic quadrilateral are supplementary?

A: We can prove this using the fact that the opposite angles of an inscribed angle are equal. Let ABCD be a cyclic quadrilateral with center O, and let angle ABD be x and angle BCD be y. Then, angle ABC is (180 – x) degrees and angle ADC is (180 – y) degrees, since angles on a straight line add up to 180 degrees. By the inscribed angle theorem, angle ABC is equal to angle AOC, and angle ADC is equal to angle AOD. Therefore, we have:

x + y = angle ABD + angle BCD = angle AOC + angle AOD = angle AOC + (180 – angle AOC) = 180 degrees

Thus, we have shown that the opposite angles of a cyclic quadrilateral are supplementary.

5. What are some examples of real-world applications of cyclic quadrilaterals?

A: Cyclic quadrilaterals are used in a variety of fields, including engineering, architecture, and physics. For example, the design of the circular gears used in many mechanical systems is based on the properties of cyclic quadrilaterals. In architecture, the shape of many domes and arches is based on the geometry of cyclic quadrilaterals.

Introduction

Heat in an object does not remain stationary and tends to move from high-temperature to low-temperature areas. Thus, overheated materials tend to cool down while cold materials tend to absorb heat from the environment and warm up. Similarly, when two objects at different temperatures come into contact, heat energy is transferred from the hotter object to the cooler one. You might have seen dogs sticking out their tongues while panting. This helps them cool down because when they inhale, moisture in the air condenses on their tongues, forming liquid droplets that later evaporate. This evaporation requires thermal energy, which is supplied by their tongues, aiding them in cooling down.

Evaporation

Dogs cool themselves

What is conduction?

Conduction refers to the transfer of heat, electricity, or energy between particles of a substance without movement of the particles across regions of different temperatures themselves. It occurs in solids, liquids, and gases, and is the primary source of heat transfer inside solids. Since the atoms inside metals are placed close together, they conduct electricity well. Physically, conduction occurs by vibration. When a solid object is heated, its atoms/molecules start vibrating rapidly. However, since each atom or molecule is bonded to the next one, this vibration causes the neighbouring atoms to vibrate, and the process continues till the heat energy has spread across the whole solid.

Mode of conduction

Conduction occurs when there is a difference in temperatures across different portions of a material. Metals conduct heat very well whereas, liquids and solids tend to make bad conductors of heat. Furthermore, heat conduction is better when the surface area of the solid is large.

Thermal Conductivity

Thermal conductivity measures an object’s ability to transmit heat. It refers to the rate of heat transfer per unit time between the two ends of an object, given a specific cross-sectional area. We know that heat always flows from a higher temperature region to a lower temperature region. Suppose we were given a uniform shaft with length ‘l’ and cross-sectional area A. If the temperature at the two ends of the shaft were ,

, and Q amount of heat was transferred through the shaft, then it is natural that Q would be proportional to the temperature difference, the cross-sectional area, and the time taken for the conduction to occur. Further, it would be inversely proportional to the length of the shaft. Hence, we can say that

Here, K is the constant of proportionality known as the thermal conductivity.

What is convection?

Convection refers to the transfer of heat by the movement of particles in a medium from the hotter region to the colder region. It is a common way of heat transfer in liquids and gases. For instance, in a hot air balloon, the air molecules at the bottom of the balloon heat up and rise, creating low-density hot air that fills the balloon and causes it to ascend. Meanwhile, the cold air at the top of the balloon moves downward as the hot air rises, thus creating a continuous cycle of air movement.

Hot air balloons 

Mode of Convection

1. Chimneys are placed above stoves since hot molecules from our cooking will rise up and reach it via convection.
2. Land and sea breeze flow based on convection. The land gets warmer faster than the sea, causing air molecules above it to rise up. The cool air from the sea flows in to maintain a pressure balance. The reverse process occurs at night.

What is radiation

Radiation is the transfer of heat without the need for particles or a medium to carry it. For instance, thermal radiation is how the sun transfers heat to the earth. During the process of radiation, heat is emitted from hot objects in all directions and unlike conduction and convection, radiation can take place even in a vacuum since it doesn’t require any a medium. Radiation of heat occurs in the form of electromagnetic radiation. Hot objects emit radiation in all directions, which is responsible for carrying heat and allows the heat energy to reach different places without the need of a medium.

Examples of conduction, convection, and radiation

1. Metals are excellent conductors of heat, which makes them perfect for cooking. On the other hand, since wool is a bad conductor, we use it in our sweaters, which keeps the heat in.
2. Thermometers utilise mercury, which is also an excellent conductor.
3. Hot air balloons use the process of convection to function as described earlier.
4. We are advised to use bright colours in summers since they reflect the heat energy coming to us in the form of radiation. Similarly, aircrafts are made up of bright colours so that they reflect whatever heat energy is incident on them.

Summary

Heat can be transferred between objects of different temperatures through convection, conduction, and radiation. Conduction occurs in solids while convection occurs in liquids and gases. Radiation can occur without the need for a medium. An example of convection is that of sea breeze and land breeze. During the day, land surfaces become warmer than seawater, causing the hot air to rise and cooler air to move towards the land at night. Temperature can be measured using Fahrenheit, Celsius, and Kelvin scales. The amount of heat energy in an object depends on the material’s mass, the temperature difference, and the material’s properties.

 

Frequently Asked Questions

1. What is Widemann-Franz Law?

This law states that the thermal and electrical conductivities of metals are directly proportional to their temperature, and at a specific temperature, they are equal.

2. What is Black body radiation?

A black body is a material that absorbs all radiation incident upon it. When held at a constant temperature, it emits all of the absorbed energy. The emitted radiation is independent of the material’s properties and is called black body radiation and it is emitted uniformly in all directions.

3. What is Stefan-Boltzmann law?

This law states that the heat energy emitted from a perfectly black body is proportional to the fourth power of temperature.

4. What happens when an ice cube is placed in water?

The process of conduction takes place when an ice cube is immersed in water. Heat from the water flows into the ice cube and melts it.
5. Discuss cooling via evaporation

Evaporation is a process wherein a liquid substance absorbs heat and changes into a gaseous state. Since heat energy is required for this to occur, evaporation can take away excess heat from objects and cool them down.

Introduction

Reflection is a phenomenon wherein, when a wave hits a surface, it does not get absorbed. Instead, the incident energy is sent back from the surface. Metal surfaces can reflect as much as 80-90% of the light when highly polished and most commonly, mirrors are made using a silver coating that is deposited on the backside of the glass. The Hale Telescope located atop Mount Palomar in California is the world’s most reflective surface.

Similarly, refraction occurs when a wave crosses from one medium to another, which changes its direction and speed. One of the most commonly used optical devices is a lens, which is formed by the intersection of two spherical surfaces.

What is a lens?

A lens is one of the most commonly used optical devices made up of two intersecting spherical surfaces. The lens is said to be thin when the distances between the surfaces become small and it is not necessary for both of the surfaces to be spherical. In fact, one of them can be a plane as well. The line joining the centre of the two surfaces is known as the principal axis and the plane through this axis is known as the principal section of the lens. A point that lies on the principal section is known as the optical centre.

There are two types of lenses: Converging lenses, and diverging lenses.

Types of lens

Difference between Lens and Mirror

What is the concave lens? 

A concave lens is a type of lens that diverges a straight light beam, creating a virtual image that is smaller than the object itself. Both sides of the concave lens are curved inwards, giving it a concave shape. Due to this shape, these lenses are also known as diverging lenses as they cause light rays to spread out. For instance, when a ray coming from the sun falls on a concave lens parallel to the principal axis, it appears to emanate from a point on the principal axis known as the primary focal point of the lens.

Similarly, when a parallel ray is emitted from the opposite side of the lens, it will also appear to converge to the primary focal point, typically denoted by the letter ‘F’. Further, a light beam originating from the focal point will become parallel to the principal axis after passing through the lens.

Lens formula for concave lens

The lens formula is an equation applicable to all types of lenses and relates the distance of the object (u), the image distance (v), and the focal length of the lens. In the form given below, it is valid only for a thin lens but formulae for thick lenses have also been derived:

What is the convex lens?

A convex lens protrudes outwards on both sides and is thicker in the centre and thinner at the edges. It is called convex because it concentrates the light falling on it. When a light beam parallel to the primary axis falls on the lens, it passes through the primary focal point on the other side. Similarly, when a light beam originates from the primary focal point and hits the lens, it emerges parallel to the principal axis. 

One common example of the effects of this lens may be seen when it is held towards the sun and sunlight is focused on a piece of paper. The sharp, radiant image of the sun obtained this way is bright and has concentrated all the light rays in one point. This concentration is strong enough to burn the paper and the images formed this way are called real images.

Lens formula for convex lens

The lens formula for convex lenses is the same as that for concave lenses. That is,

Uses of convex and concave lens

Convex Lens

1. Convex lenses are used to manufacture magnifying glasses. 
2. Microscopes utilise convex lenses.
3. People suffering from hypermetropia are prescribed convex lenses, which can help focus the image correctly on the retina.
4. Convex lenses are also used in cameras.

Concave lens

1. Just like hypermetropia, myopia is corrected by using concave lenses.
2. Flashlights, binoculars, telescopes, eyeglasses, etc. are common devices that use concave lenses. 

Summary

A lens is a translucent medium formed by the intersection of two spherical surfaces or a spherical and a plane surface. When the surfaces are close, a thin lens is formed. There are two types of lenses: convex and concave. A convex lens protrudes outwards on both sides and is wide in the centre and narrow at the edges. A concave lens is bent inward on both sides and diverges the light rays that pass through it, earning it the name of diffuse lens. Ordinary mirrors are silver-coated on the back of glass. The Hale Telescope on Mount Palomar, California is the world’s largest reflector.

 

Frequently Asked Questions 

1. What is the law of light reflection?

There are two statements related to the law of reflection:

1. The incident ray, the reflected ray, and the surface normal will lie in one single plane.
2. The angle made by the incident and reflected rays with the vertical will be equal.

2. Define the power of a lens.

The power of a lens physically means its ability to bend light. Mathematically, it is measured as the inverse of the focal length of the lens.

 3. Calculate the power of a lens made of glass with a focal length of 150cm.

Given; Focal length 

Since the focal length and thus, the power is positive, this lens is concave.

4. What is Prism?

A prism is a solid object made of high quality glass, consisting of three non-parallel rectangular planes. One of these planes is the base, while the other two are polished and known as the refracting surfaces. The rough surface is called the base and the prism is made by joining all three surfaces to form a 3D triangle of sorts.

5. The focal length of the concave lens is 15cm. If an image is to be formed at 10 cm, how far should the object be placed from the lens?

We are given that

 v=-10 cm         f=-15 cm

Our job is to find u, which can be done via the lens formula

Thus, the image must be placed 30 cm to the left of the lens.

6. State Two Differences Between a Convex and a Concave Lens ?

1. Shape:

• Convex Lens: A convex lens is thicker in the middle and thinner at the edges. It has a shape that bulges outward, like the exterior of a sphere. It is also referred to as a converging lens because it focuses parallel light rays towards a single point.
• Concave Lens: A concave lens is thinner in the middle and thicker at the edges. Its shape curves inward, resembling the interior of a sphere. This type of lens is also called a diverging lens because it spreads parallel light rays away from each other.

2. Focal Point and Image Formation:

• Convex Lens: When parallel light rays pass through a convex lens, they converge or come together at a single point known as the focal point. Convex lenses can form both real and virtual images, depending on the object’s distance from the lens. Real images are formed when the object is placed beyond the focal length and are inverted, while virtual images are formed when the object is placed within the focal length and are upright.
• Concave Lens: When parallel light rays pass through a concave lens, they diverge or spread out. As a result, concave lenses only form virtual, upright, and reduced images. The focal point of a concave lens is the point from which the diverging rays appear to originate when extended backward.

Introduction

There are two types of mirrors – flat and curved. Flat mirrors are commonly used in homes while curved mirrors have specific applications in science and industry. Curved mirrors are classified into two types – concave and convex. The concave mirror has an inward curve and resembles a broken arc of a hollow sphere, while for the convex mirror, the reflecting surface is on the outside. Such special types of mirrors find widespread applications. For instance, when we need a wide-angle view, we can use convex mirrors and scientists can also use curved mirrors while designing telescopes and optical instruments.

Concave Mirror with Diagram and Formula

A concave mirror is curved inward on its inner reflecting surface and thus, you will see that it resembles the inside of a cave. The key parameters of concave mirrors are similar to those of a sphere, including the centre of curvature, the radius of curvature, the principal focus, and the focal length. To understand these terms better, take a look at the diagram below, which illustrates each of these parameters. We have shown the concave mirror detached from its parent sphere to aid in your understanding.

Concave mirror

Light rays coming from an object can reach the mirror one out of three ways:

1. It can pass through the focal point and hit the mirror. In such a case, reflection makes it parallel to the principal axis.
2. A light ray that crosses the centre of curvature before hitting the mirror will retrace the path it took initially.
3. Light rays can also hit the mirror while travelling parallel to the principal axis. Such rays will cross the focal point of the lens after reflection.
4. Finally, if a ray doesn’t satisfy either of the above two criteria, it will reflect from the mirror following the law of reflection, i.e., the angle of incidence will be the same as the angle of reflection.

Except for when the object is placed between the focal point and the pole of the mirror, concave mirrors produce a real and inverted image. Two possible ways of creating an image using this mirror are shown below:

Concave mirror

Concave mirror

One common example of the use of this mirror is in flashlights and torches, which use a concave mirror around the bulb, making the output beam parallel to the principal axis.

Example: For an object placed 90 cm from a concave mirror of focal length 30 cm. What is the distance at which the image will be formed?

It is a common norm to use u and v to represent the image and object distances, respectively. If f is the focal length of the mirror, then the mirror formula reads:

While performing measurements, certain sign conventions are followed. These are stated in the diagram below:

Hence, we have:

 

Thus, the image will be formed 45 cm towards the left side of the mirror.

Convex Mirror with Diagram and Formula

A convex mirror has a reflecting surface that is curved outward and is characterised by the same parameters as its concave counterpart. Thus, concepts like the centre of curvature, pole, radius of curvature, focus, etc. are present here as well and defined similarly. The mirror formula remains the same but the object distance is taken as positive since convex mirrors tend to form a virtual image towards the right side of the mirror. We can trace the light rays for a convex mirror just like a concave mirror.

Convex mirror ray tracing

The following properties may be noted for a convex mirror:

• A ray incident parallel to the principal axis will seem to emanate from the focal point.
• Light rays that fall on the pole of the mirror at an angle will be reflected on the other side of the principal axis at the same angle.
• A ray that seems to hit the centre of curvature of the mirror will not be deflected.
  

Characteristics Of Concave and Convex Mirror

Concave mirror

The images formed via a concave mirror can be seen in the diagram below, which illustrates the characteristics of this mirror. Objects placed in front of the mirror are represented in red while the images formed are represented in blue.

We can draw the following inferences:

• When the object is placed beyond the focal point of the mirror, a virtual image is formed behind the mirror.
• For an object placed at the focal point, no image is formed.
• For an object placed at the centre of curvature, an inverted image is formed at the centre of curvature itself.

Concave mirror

Description: Different image characteristics for a concave mirror.

Convex mirror

Just as in the case of a concave mirror, we can perform similar analysis for a convex mirror as well. Ray Tracing allows us to determine how different objects will appear. Generally, a convex mirror forms virtual images.

Convex mirror

For a convex mirror, the images formed are virtual and thus impossible to project on a screen. 

Convex mirror

Uses Of Concave and Convex Mirror

Uses of Concave Mirrors:

1. Vehicle Headlights: Concave mirrors are used in vehicle headlights to direct the light from the bulb into a parallel beam, improving visibility on the road.
2. Shaving and Makeup Mirrors: Concave mirrors provide a magnified and upright image when the object is placed within the focal length, making them ideal for close-up tasks like shaving or applying makeup.
3. Ophthalmoscopes: Ophthalmologists use concave mirrors in ophthalmoscopes to examine the interior of a patient’s eye, including the retina and optic nerve.
4. ENT Examination: Concave mirrors are used by ENT doctors to focus light into the patient’s ear, nose, or throat, making it easier to examine these areas.
5. Solar Concentrators: Concave mirrors are used in solar concentrators to focus sunlight onto a small area, such as a solar cell or a heat-absorbing target, maximizing the energy collected.

Uses of Convex Mirrors:

1. Rear-View Mirrors in Vehicles: Convex mirrors are used as rear-view mirrors in automobiles because they provide a wider field of view, allowing drivers to see more of the area behind the vehicle. However, objects appear smaller and farther away in a convex mirror, so caution must be exercised while judging distances.
2. Security Mirrors: Convex mirrors are used in ATMs, retail stores, and other locations for security purposes. Their wide field of view allows surveillance of large areas with a single mirror, making it easier to monitor activity and spot potential security issues.

Difference Between Concave and Convex Mirror

Summary

With only slight differences in construction, concave and convex mirrors lead to vastly different images, which makes them quite interesting and useful in several applications. In this article, we discussed the various factors which were common across these two types of mirrors and showcased the diagrams, formulae, and uses of both. Further, we tabulated the differences in their properties and characteristics.

 

Frequently Asked Questions

1. What is magnification?

Magnification measures the increase or decrease in size of the image as compared to the size of the object. It is defined as the ratio of height of image to height of object.

2.  What is the focal plane?

The focal plane is defined as that plane which lies perpendicular to the principal axis and passes through the focal point of the lens.

3. What is aperture?

The aperture measures the size of the mirror, and it is the diameter of the mirror itself.

4. What happens when an object is taken farther away from a concave mirror?

For a concave mirror, the image size becomes smaller and smaller as the object is pulled farther and farther from the mirror.

5. What does the value of magnification indicate?

The sign of magnification can tell us whether the image is erect or inverted. Further, its magnitude is greater than 1 if the image is magnified or less than 1 if diminished.

जिन वाक्यों में किसी विशेष शब्द के द्वारा खुशी, दुख, घृणा, आश्चर्य आदि के भाव व्यक्त हो, उन्हें विस्मयादिबोधक वाक्य कहते हैं। विस्मयादिबोधक को एक चिन्ह (!) से भी प्रकट करते है। जिसे विस्मयादिबोधक चिन्ह कहते है।

 उदाहरण-

‘अरे! इतनी मोटी पुस्तक।’

इस वाक्य में अरे शब्द के द्वारा आश्चर्य को दर्शाया गया है और विस्मयादिबोधक चिन्ह भी लगाया गया है। इसलिए यह विस्मयादिबोधक वाक्य है।

-‘ओह! सुनकर दुख हुआ।’

 इस वाक्य में ओह के द्वारा दुख का बोध कराया गया है तथा ! चिन्ह भी लगाया गया है। यह विस्मयादिबोधक वाक्य है।

-‘छिः! कितनी गंदगी है।’

इस वाक्य में छी शब्द के द्वारा घृणा का भाव व्यक्त किया गया है। इसमें ! चिन्ह का भी प्रयोग किया गया है। इसलिए यह विस्मयादिबोधक वाक्य है।

-‘शाबाश! बहुत बढ़िया|’

इस वाक्य में शाबाश शब्द के द्वारा खुशी को व्यक्त किया गया है और ! चिन्ह का भी प्रयोग है। इसलिए यह वाक्य विस्मयादिबोधक वाक्य है।

विस्म्यादिवाचक वाक्यों में किसी तीव्र भावना को जताने के लिए जो शब्द इस्तेमाल किये जाते हैं उन्हें विस्मय बोधक शब्द कहते हैं।

इन विस्मयादिबोधक को प्रकट करने के लिए कुछ शब्दों का प्रयोग किया जाता है जो इस प्रकार है।

-अरे! (आश्चर्य व्यक्त करने के लिए)

‘अरे! तुम कब आए।’

इस वाक्य में किसी के आने से आश्चर्य को प्रकट करने के लिए अरे शब्द का प्रयोग किया गया है, जो विस्मयादिबोधक शब्द है।

-‘अरे! इतनी सुंदर चित्रकारी।’

इस वाक्य में अरे के द्वारा सुंदर चित्रकारी के प्रति आचार्य का भाव प्रकट किया गया है। 

कई बार ‘अरे’ शब्द का प्रयोग संविधान के लिए भी होता है।

उदाहरण:

-‘अरे! मोहन बाहर गए है।’

यहाँ पर मोहन को संबोधित करते हुए इसमें बारे में अरे विस्मयादिबोधक शब्द का प्रयोग कर के बाहर जाने की बात कही गई है।

-अरे यार! ( दुख प्रकट करने के लिए) 

‘अरे यार! मेरा काम तो पूरा ही नहीं हुआ।’

 इस वाक्य में काम के पूरा न होने पर दुख हुआ है जिसे अरे यार! शब्द से प्रकट किया गया है।

-ओह! ( शोक व्यक्त करने के लिए)

‘ओह! उसके साथ बहुत बुरा हुआ।’

दिए गए वाक्य में किसी के साथ बुरा होने पर दुख हुआ है जिसे ओह विस्मयादिबोधक शब्द से दर्शाया गया है।

-‘ओह! मेरे हाथ में दर्द है।’

इस वाक्य में ओह के द्वारा हाथ में दर्द अर्थात शोक को दर्शाया गया है।

-छिः! ( घृणा व्यक्त करने के लिए) 

 ‘छी! अमित के कपड़े कितने गंदे है।’

 यहाँ पर अमित के गंदे कपड़ो के प्रति घृणा दिखाई गई है।जिसे छी शब्द द्वारा बताया गया है।

-‘छी! कितना गन्दा फर्श है।’

यहाँ वाक्य में छी शब्द के द्वारा फर्श के प्रति घृणा को दर्शाया गया है। इसलिए यह विस्मयादिबोधक शब्द है।

-शाबाश! ( खुशी व्यक्त करने के लिए)

‘शाबाश! तुमने अच्छा काम किया है।’

इस वाक्य में किसी के द्वारा अच्छा काम करने पर खुशी को व्यक्त करने के लिए शाबाश विस्मयादिबोधक शब्द का प्रयोग किया गया है।

-‘शाबाश! देखो अमित प्रथम आया।’

इस वाक्य में अमित के प्रथम आने की खुशी प्रकट करने के लिए शाबाश शब्द का प्रयोग किया गया है। जोकि विस्मयादिबोधक शब्द है।

-ये क्या! ( आश्चर्य व्यक्त करने के लिए)

‘ये क्या! राम अभी तक गया नहीं।’

यहाँ पर राम के न जाने के कारण आश्चर्य का भाव ये क्या विस्मयादिबोधक शब्द से दर्शाया गया है।

-‘ये क्या! तुमने अभी तक खाना नहीं बनाया।’

इस वाक्य में खाना नहीं बनाने पर ये क्या विस्मयादिबोधक शब्द द्वारा आश्चर्य प्रकट किया गया है। इसलिए यह विस्मयादिबोधक शब्द है।

-हाय! ( दुख व्यक्त करने के लिए)

‘हाय! मीरा को बहुत चोट आई है।’

इसमें मीरा को चोट आने में दुख हुआ है, जिसे हाय विस्मयादिबोधक शब्द से दर्शाया गया है।

-‘हाय! अमित के बिना मैं अब क्या करूँगी।’

इस वाक्य में अमित के बिना रहने का दुख प्रकट करने के लिए हाय! विस्मयादिबोधक शब्द का प्रयोग किया गया है।इसलिए यह हाय विस्मयादिबोधक शब्द है।

-हे भगवान! ( शुक्रिया, दुख व्यक्त करने के लिए)

‘हे भगवान! तुमने बचा लिया।’

इस वाक्य में जान बचाने के लिए भगवान को धन्यवाद किया गया है।

-‘हे भगवान! तूने मेरे साथ ऐसा क्यों किया।’

इस वाक्य में किसी के साथ कुछ गलत होने पर दुख प्रकट करने के लिए हे भगवान विस्मयादिबोधक शब्द का प्रयोग किया है।

-काश! ( इच्छा व्यक्त करने के लिए)

‘काश! मैं भी घूमने जाती।’

यहाँ पर घूमने की इच्छा काश विस्मयादिबोधक शब्द के द्वारा बताई गई है। 

-‘काश! मेरा पूरा परिवार साथ होता।’

इस वाक्य में पूरा परिवार साथ होने की इच्छा प्रकट की गई है। जिसके लिए काश विस्मयादिबोधक शब्द का प्रयोग किया गया है।

-क्या ! (प्रश्न पूछने के लिए)

‘क्या! तुमने खाना नही खाया।’

यहाँ पर खाना नहीं खाने का प्रश्न क्या विस्मयादिबोधक शब्द के द्वारा पूछा गया है।

– ‘क्या! वह तुम्हारे साथ जायेगा।’

इस वाक्य में किसी के साथ जाने का प्रश्न क्या विस्मयादिबोधक शब्द के द्वारा पूछा गया है।

ये सभी विस्मयादिबोधक शब्द है जिनका प्रयोग तिरस्कार, संबोधन, भय, हर्ष, स्वीकृत, शोक आदि के लिए प्रयोग किए जाते है। जिनसे हम किसी भी इंसान की भावनाओं को आसानी से समझ सकते है।

अधिकतर पूछें गए प्रश्न–:

1. विस्मयादिबोधक किसे कहते है?

उत्तर: जिन वाक्यों में किसी विशेष शब्द के द्वारा खुशी, दुख, घृणा, आश्चर्य आदि के भाव व्यक्त हो, उन्हें विस्मयादिबोधक वाक्य कहते हैं। विस्मयादिबोधक को एक चिन्ह (!) से भी प्रकट करते है। जिसे विस्मयादिबोधक चिन्ह कहते है।

2. विस्मयादिबोधक शब्द किसे कहते है?

उत्तर: विस्म्यादिवाचक वाक्यों में किसी तीव्र भावना को जताने के लिए जो शब्द इस्तेमाल किये जाते हैं उन्हें विस्मय बोधक शब्द कहते हैं। यह शब्द निम्नलिखित है–:

अरे, काश, छी, हे भगवान, हाय, ओह, क्या, ये क्या, शाबाश, अच्छा, अरे यार,

3. ’काश! मैं अब अपने घर जा पाती।’

वाक्य में कैसा विस्मयादिबोधक सूचक है।

उत्तर: दिए गए वाक्य में काश! विस्मयादिबोधक सूचक है। इसमें काश के द्वारा घूमने की इच्छा प्रकट की गई है। यह एक विस्मयादिबोधक शब्द है।

4. दुख को किस विस्मयादिबोधक सूचक द्वारा व्यक्त किया जाता है।

उत्तर: दुख को हे भगवान, हाय, अरे यार आदि विस्मयादिबोधक शब्दों के द्वारा व्यक्त किया जाता है।

5. आश्चर्य को किस विस्मयादिबोधक द्वारा व्यक्त किया जाता है।

उत्तर: आश्चर्य को अरे!, ये क्या! आदि विस्मयादिबोधक शब्दों के द्वारा व्यक्त किया जाता है।

इन्हे भी पढ़िये

सर्वनाम	संज्ञा
प्रत्यय	अलंकार
वर्तनी	पद परिचय
वाक्य विचार	समास
लिंग	संधि
विराम चिन्ह	शब्द विचार
अव्यय	काल

जो शब्द किसी एक शब्द का संबंध किसी दूसरे शब्द से बताते है उसे संबंध बोधक कहते है।

संबंध बोधक में संज्ञा या सर्वनाम का संबंध वाक्य के अन्य शब्दों से दर्शाया जाता है उसे संबंधबोधक अव्यय कहते हैं।

 जैसे: के ऊपर, के बाद, हेतु, लिए, कारण, मारे, चलते, संग, साथ, सहित, बिना, बगैर, अलावा, अतिरिक्त, के बाद, बदले, पलटे, आगे, पीछे, इधर, उधर पास-पास इत्यादि संबंधबोधक अव्यय हैं।

उदाहरण: ‘पेड़ पर बिल्ली बैठी है।’

 ‘मोहन गीता के साथ घूमने गया।’

इन वाक्यों में पर, के साथ आदि संबंध बोधक शब्दों का प्रयोग किया गया है। जो संज्ञा और सर्वनाम का वाक्य के दूसरे शब्दो से संबंध बताता है।

हिंदी में बहुत से संबंधबोधक अव्यय उर्दू और संस्कृत से आए हैं. जैसे:

उर्दू से आए हुए संबंधबोधक अव्यय –  भर, रूबरू, नजदीक, सबब, बदौलत, बाद, तरह, खिलाफ, खातिर, बाबत, जरिए, बदले, सिवा इत्यादि।

संस्कृत से आए हुए संबंधबोधक अव्यय – संभव,  समक्ष, सम्मुख, निकट, समीप, कारण, उपरांत, अपेक्षा, भांति, विपरीत, निमित्त, हेतु, द्वारा, विषय, बिना, अतिरिक्त इत्यादि।

उदाहरण-  ‘सैनिक अपने देश की खातिर अपने प्राण भी दे देते हैं।’

‘रात भर जागना अच्छा नहीं होता।’

‘जल के बिना जीवन संभव नहीं है।’

‘विद्यालय में बच्चे अनेक विषय पढ़ते है।’

वाक्यों में की खातिर,भर, संभव और विषय उर्दू और संस्कृत भाषा के संबंध बोधक शब्दों का प्रयोग किया गया है।

सम्बन्ध बोधक अव्यय के भेद –( Sambandh Bodhak Avyay ke Bhed)

प्रयोग के आधार पर सम्बन्धबोधक अव्यय दो प्रकार के होते 

संबद्ध सम्बन्धबोधक अव्यय

अनुबद्ध सम्बन्धबोधक अव्यय

1. संबद्ध सम्बन्धबोधक अव्यय –

किसी वाक्य में संज्ञा शब्दों की विभक्तियों के पीछे इन अव्यय पदों का प्रयोग किया जाता है, उन्हें संबद्ध सम्बन्धबोधक अव्यय कहते हैं। 

सम्बन्धबोधक अव्ययों का प्रयोग किसी कारक चिन्ह के बाद किया जाता है

जैसे: घर के बिना, भोजन से पहले आदि।

 उदाहरण:  ‘ज्ञान के बिना मुक्ति नहीं मिलती है।’

               ‘धन के बिना जीवन मुश्किल है।’

इन शब्दों में के बिना बोधक शब्द का प्रयोग किया गया है।

2. अनुबद्ध सम्बन्धबोधक अव्यय –

 इन शब्दों का प्रयोग संज्ञा के विकृत रूप के साथ किया जाता है उन्हें अनुबद्ध सम्बन्धबोधक अव्यय कहते हैं। 

जैसे: दोस्तों सहित, किनारे तक,पुत्रों समेत आदि।

उदाहरण: ‘नहर का पानी किनारे तक आ गया।’

             ‘अवनी मित्रों सहित शिमला घूमने गई है।’

इन शब्दों में किनारे तक, सहित आदि बोधक शब्दों का प्रयोग किया गया है।

हिंदी में मुख्य रूप से प्रयोग किए जाने वाले संबंध बोधक शब्द दस प्रकार के होते हैं-

1. कालवाचक संबंधबोधक अव्यय
2. स्थानवाचक संबंधबोधक अव्यय।
3. दिशावाचक संबंधबोधक अव्यय।
4. साधनवाचक संबंधबोधक अव्यय।
5. हेतुवाचक संबंधबोधक अव्यय।
6. समतावाचक संबंधबोधक अव्यय।
7. पृथकवाचक संबंधबोधक अव्यय।
8. विरोधवाचक संबंधबोधक अव्यय।
9. संगवाचक संबंधबोधक अव्यय। 
10. तुलनवाचक संबंधबोधक अव्यय।

1. कालवाचक संबंधबोधक अव्यय

जिन शब्दों के द्वारा वाक्यों में समय का पता चलता है उसे काल वाचक अव्यय कहते है।

जैसे: के बाद, से पहले, 

उदाहरण: वह मोहन से पहले घर पहुंच गया था।

2. स्थानवाचक संबंधबोधक अव्यय

जिन वाक्यों में किसी की स्थिति या स्थान का पता चलता है, उसे स्थानावाचक बोधक कहते है।

जैसे: के बीच में, के पास में

उदाहरण: अमित के पास एक कुत्ता खड़ा है।

3. दिशावाचक संबंधबोधक अव्यय

जिस शब्दों के द्वारा किसी की स्थिति का ज्ञान या उसकी दिशा का पता चलता है, उसे दिशा वाचक बोधक कहते है।

जैसे: की तरफ, के सामने, के पास, 

उदाहरण: सूर्य पूर्व की ओर से उगता है।

4. साधनवाचक संबंधबोधक अव्यय

इन शब्दों के द्वारा किसी साधन या जरिए का बोध होता है।

जैसे: के जरिए, के माध्यम, के द्वारा, के साथ

उदाहरण: अरुणा रेलगाड़ी के माध्यम से दिल्ली पहुंची

5. हेतुवाचक संबंधबोधक अव्यय

इन शब्दों के द्वारा वाक्य में किसी कारण का बोध होता है।

जैसे: के लिए, के वास्ते, के खातिर

उदाहरण: राज में मां के लिए शराब पीना छोड़ दिया।

6. समतावाचक संबंधबोधक अव्यय

जिन शब्दों के द्वारा वाक्य में समानता का बोध होता है, उसे समता वाचक बोधक कहते है।

जैसे:  के बराबर, के तरह, के जैसा

7. पृथकवाचक संबंधबोधक अव्यय

जिन शब्दों के द्वारा किसी से अलग या भिन्न होने का पता चलता है, उसे पृथकवाचक बोधक कहते है।

जैसे: से अलग, से हटकर, से दूर)

उदहारण: तुम अपनी बहन से अलग हो।

8. विरोधवाचक संबंधबोधक अव्यय

इन शब्दों के द्वारा वाक्य में विरोध का ज्ञान होता है।

जैसे: के विरोध, के विपरीत

उदाहरण: तुम अपने पिता की बातों से विपरीत काम क्यों करते हो।

9. संगवाचक संबंधबोधक अव्यय

इन शब्दों के द्वारा वाक्यों में साथ नजर आता है।

जैसे: के साथ, के संग

उदाहरण: मैं अपने पिता के साथ गई थी

10. तुलनवाचक संबंधबोधक अव्यय

इन शब्दों के द्वारा वाक्यों। में तुलना की जाती है।

जैसे: के अपेक्षा, के सामने

उदाहरण: ताज महल के सामने कोई भी इमारत सुंदर नहीं है।

अधिकतर पूछे गए प्रश्न:

1. संबंध बोधक किसे कहते है?

उत्तर: जो शब्द किसी एक शब्द का संबंध किसी दूसरे शब्द से बताते है उसे संबंध बोधक कहते है।

संबंध बोधक में संज्ञा या सर्वनाम का संबंध वाक्य के अन्य शब्दों से दर्शाया जाता है उसे संबंधबोधक अव्यय कहते हैं।

 जैसे: के ऊपर, के बाद, हेतु, लिए, कारण, मारे, चलते, संग, साथ, सहित, बिना, बगैर, अलावा, अतिरिक्त, के बाद आदि।

2. संबंध बोधक के कितने भेद है?

उत्तर: प्रयोग के आधार पर सम्बन्धबोधक अव्यय दो प्रकार के होते 

संबद्ध सम्बन्धबोधक अव्यय

अनुबद्ध सम्बन्धबोधक अव्यय

3. हिंदी में कितने प्रकार के संबंध बोधक प्रयोग किए जाते है?

उत्तर: हिंदी में मुख्य रूप से प्रयोग किए जाने वाले संबंध बोधक शब्द दस प्रकार के होते हैं।

1. कालवाचक संबंधबोधक अव्यय
2. स्थानवाचक संबंधबोधक अव्यय।
3. दिशावाचक संबंधबोधक अव्यय।
4. साधनवाचक संबंधबोधक अव्यय।
5. हेतुवाचक संबंधबोधक अव्यय।
6. समतावाचक संबंधबोधक अव्यय।
7. पृथकवाचक संबंधबोधक अव्यय।
8. विरोधवाचक संबंधबोधक अव्यय।
9. संगवाचक संबंधबोधक अव्यय। 
10. तुलनवाचक संबंधबोधक अव्यय।

4. अरुणा की अपेक्षा करुणा सुंदर है।

दिए गए वाक्य में कौन सा बोधक शब्द है?

उत्तर: दिए गए वाक्य में अरुणा की अपेक्षा करुणा शब्दों के माध्यम से अरुणा की तुलना करुणा से की गई है। इसलिए इस वाक्य में तुलनाबोधक शब्द है।

5. समता वाचक बोधक में कौन से शब्दों का प्रयोग किया जाता है?

उत्तर: समता वाचक बोधक शब्द वाक्य में समानता को दर्शाते है। इसलिए इसके लिए की तरह, के जैसा आदि शब्दों का प्रयोग किया जाता है।

इन्हे भी पढ़िये

सर्वनाम	संज्ञा
प्रत्यय	अलंकार
वर्तनी	पद परिचय
वाक्य विचार	समास
लिंग	संधि
विराम चिन्ह	शब्द विचार
अव्यय	काल

वे शब्द जो दो शब्दों अर्थात एक शब्द को दूसरे शब्द से वाक्यांशों या वाक्यों, एक वाक्य को दूसरे वाक्य से जोड़ते हैं समुच्चयबोधक कहते हैं।

जैसे: और, बल्कि, तथा, अथवा, यदि, किंतु, अन्यथा, हालांकि, लेकिन, इसलिए आदि|      

 उदाहरण: 

1. ‘अमित और देव सो रहे हैं।’

इस वाक्य में अमित, देव को एक दूसरे से जोड़ा गया है। इन्हे जोड़ने के लिए और शब्द का प्रयोग किया गया है।            

2. ‘वह प्यासा था, इसलिए उसने पानी पिया।’

इस वाक्य में दो वाक्यों को इसलिए शब्द से जोड़ा गया है। यह समुच्चय बोधक शब्द है।

1. समानाधिकरण समुच्चयबोधक
2. व्यधिकरणसमुच्चयबोधक

1. समानाधिकरण समुच्चयबोधक

जो समुच्चयबोधक अव्यय दो स्वतंत्र वाक्यों या उपवाक्यों को जोड़ते हैं, उन्हें समानाधिकरण सममुच्चबोधक अव्यय कहा जाता है। 

जैसे: परंतु, अन्यथा, अत:, किंतु, और, या, बल्कि, इसलिए, व, एवं, लेकिन आदि।

उदाहरण:-  ‘विराट और रोहित भाई है।’

इस वाक्य में विराट, रोहित दो स्वतंत्र शब्दों को और शब्द से जोड़ा गया है, जो समानाधिकरण समुच्चय बोधक शब्द है।

समानाधिकरण समुच्चयबोधक अव्यय चार प्रकार के होते हैं-

क) संयोजक

ख) विकल्पसूचक

ग) विरोधसूचक

घ) परिमाणसूचक

1. संयोजक:– जिन शब्दों से दो शब्दों या दो वाक्यों को आपस में जोड़ते हैं तथा इसमें शब्दों के द्वारा वाक्यों और वाक्यांशो को इकट्ठा करते हैं। उसे संयोजक सम्मुच्यबोधक कहते है।

 वे शब्द जिनके द्वारा शब्दों और वाक्यों को इक्कठा किया जाता है, वे है–: तथा, जोकि, अर्थात्, और, एवं शब्द संयोजक कहलाते हैं।

उदाहरण:-‘राहुल और अंजली वहां खड़े है|’

इस वाक्य में राहुल, अंजली को जोड़ने के लिए और शब्द का प्रयोग किया गया है, जोकि संयोजक शब्द है।

2. विकल्पसूचक: जिन शब्दों के द्वारा वाक्य में विकल्प, दो या दो अधिक का चयन दिया जाता है, उसे विकल्प सूचक कहते है। इन शब्दों से विकल्प का पता चलता है।

जैसे–: या, वरना, अथवा, वा, चाहे शब्द विकल्पसूचक कहलाते हैं।

उदाहरण:- “मोहन यहां सो सकता है अन्यथा श्याम सो जाएगा|’

इस वाक्य में मोहन के सोने के साथ साथ श्याम के सोने का भी विकल्प दिया गया है। इस अन्यथा शब्द से जोड़ा गया है जो विकल्पसूचक शब्द है।

3. विरोध सूचक: यह शब्द दो वाक्यों या दो विरोध करने वाले कथनों को आपस में जोड़ते है। इन वाक्यों में आपस में विरोध दिखाई देता है।

किंतु, लेकिन, परंतु, पर, बल्कि, अपितु शब्द विरोध सूचक कहलाते हैं।

उदाहरण:- ‘वह अमीर है परंतु बेईमान है।’

इस वाक्य में दो विरोधाभास वाक्य है। फला की वह अमीर है और दूसरा की वह बेईमान है। इन शब्दों की परंतु शब्द से जोड़ा गया है जो विरोध सूचक शब्द है।

4. परिमाणसूचक:- जिन शब्दों से वाक्य में किसी के परिमाण का पता चले तथा जो शब्द परिमाण दर्शाने वाले वाक्यों को जोड़ते हैं, उसे परिमाण सूचक कहते है।

जैसे: इसलिए, ताकि, अतः, अन्यथा, नहीं तो शब्द परिणामदर्शक कहलाते हैं।

उदाहरण:- ‘उसने अपना कार्य पूरा किया ताकि उसको डांट न पड़े।’

इस वाक्य में डांट न पड़े वाक्य को उसने कार्य पूरा किया से ताकि के द्वारा जोड़ा गया है। यह परिमाण सूचक शब्द है|

2. व्यधिकरण समुच्चयबोधक

 जो शब्द एक या एक से अधिक आश्रित उपवाक्यों को आपस में जोड़ते हैं, उन्हें व्यधिकरण समुच्चयबोधक कहते हैं। इसमें एक प्रधान और दूसरा आश्रित वाक्य होता है।

जैसे: यदि तो, क्योंकि, ताकि, कि, यद्यपि तथापि आदि।

उदाहरण:- ‘मां ने कहा कि तुम अपना काम करो।’

इस वाक्य में मां ने कहा वाक्य तुम अपना काम करो पर आश्रित है, जिसे कि शब्द से जोड़ा गया है। यह व्यधि कारण बोधक शब्द है।

व्याधिकरण समुच्चयबोधक भी चार प्रकार के होते हैं

क)कारण बोधक

ख)संकेतबोधक

ग)स्वरूपबोधक

घ)उद्देश्यबोधक

(क) कारण बोधक

 जिन शब्दों के द्वारा किसी वाक्य के कार्य करने के कारण का बोध होता है, उसे कारण बोधक कहते है।

जैसे :चूँकि, क्योंकि, कि, इसलिए, इस कारण शब्द हेतुबोधक हैं।

उदाहरण:- ‘वह सुंदर है इसलिए मुझे पसंद है।’

इस वाक्य में पसंद करने का कारण उसका सुंदर होना है। जिसे इसलिए शब्द से जोड़ा गया है, जो कारण बोधक शब्द है।

(ख) संकेतबोधक:- जिन वाक्यों में किसी घटना या कार्य के बारे में संकेत मिलते हैं, उसे ‘संकेतवाचक’ कहते हैं। इसमें पहले वाक्य का दूसरे वाक्य की शुरुआत में संकेत मिलते है।

जैसे: यदि, तो, चाहे भी, यद्यपि, तथापि शब्द संकेतबोधक है।

उदाहरण:– ‘यदि तुम कामयाब होना चाहते हो तो तुम्हें मेहनत करनी पड़ेगी।’

 इस वाक्य में कामयाब होने के लिए मेहनत करना का संकेत किया है जिसे इसने यदि और तो से जोड़ा है, को संकेतबोधक शब्द है।

(ग) स्वरूपबोधक:- जिन वाक्यों में किसी उपवाक्य का अर्थ पूर्ण रूप से स्पष्ट होता है। उन्हें ‘स्वरूपबोधक’ कहते हैं। इन शब्दों में स्पष्टीकरण आता है।

जैसे: अर्थात, यानि, मानो, यहाँ, तक, शब्द स्वरूपबोधक हैं।

उदाहरण:- ‘पंछी उन्मुक्त है अर्थात स्वतंत्र हैं।’

इस वाक्य में उन्मुक्त शब्द को स्पष्ट करने के लिए अर्थात शब्द का प्रयोग किया गया है, जोकि स्वरूपबोधक शब्द है।

(घ) उद्देश्यबोधक: जिन दो शब्दों को जोड़ने से उसका उद्देश्य स्पष्ट होता है, उसे उद्देश्यबोधक कहते हैं।इन अव्यय शब्दों से उद्देश्य का पता चलता है।

जैसे: ताकि, जिससे कि शब्द ‘उद्देश्यबोधक’ हैं।

उदाहरण:– ‘खाना खा लो ताकि भूख न लगे।’

इस वाक्य में पहला वाक्य खाना खा लो का उद्देश्य भूख न लगने से बताया जा रहा है। उद्देश्य को जोड़ने के लिए ताकि शब्द का प्रयोग किया गया है जोकि उद्देश्य बोधक शब्द है।

अधिकतर पूछे गए प्रश्न

1.समुच्चय बोधक किसे कहते है।

उत्तर:वे शब्द जो दो शब्दों अर्थात एक शब्द को दूसरे शब्द से वाक्यांशों या वाक्यों, एक वाक्य को दूसरे वाक्य से जोड़ते हैं समुच्चयबोधक कहते हैं।

2.समुच्चय बोधक के कितने भेद है।

उत्तर:समुच्चयबोधक के निम्नलिखित दो भेद होते हैं-

1. समानाधिकरण समुच्चयबोधक
2. व्यधिकरणसमुच्चयबोधक

3.व्याधिकरण समुच्चयबोधक के कितने भेद है।

उत्तर:

व्याधिकरण समुच्चयबोधक भी चार प्रकार के होते हैं-

क)कारण बोधक

ख)संकेतबोधक

ग)स्वरूपबोधक

घ)उद्देश्यबोधक

4. तुम जाना चाहो तो जाओ वरना रोहन चला जायेगा।

इस वाक्य में कौनसा का समुच्चय बोधक है।

उत्तर: इस वाक्य में विकल्प समुच्चय बोधक है। क्योंकि उसके जाने के साथ साथ रोहन के जाने का भी विकल्प दिया गया है और वरना शब्द का बोध किया गया है को विकल्प बोधक शब्द है।

5.समानाधिकरण समुच्चयबोधक के कितने भेद है।

उत्तर: समानाधिकरण समुच्चयबोधक अव्यय चार प्रकार के होते हैं-

क)संयोजक

ख)विकल्पसूचक

ग)विरोधसूचक

घ)परिमाणसूचक

सर्वनाम	संज्ञा
प्रत्यय	अलंकार
वर्तनी	पद परिचय
वाक्य विचार	समास
लिंग	संधि
विराम चिन्ह	शब्द विचार
अव्यय	काल

Introduction

Similar peoples facing similar problems. The stories used to be defined by both social practicality and sharp satire. Even though he takes great pains to represent his characters in their own words, Chaucer is also out to expose the hypocrisy of the church and the social problems that stemmed from the Middle Ages’ political and social norms.

Summary of the Canterbury Tales

In the spring, people from all walks of life gather at the Tabard Inn before setting off on a pilgrimage to Canterbury to beg favours of the English martyr St. Thomas à Becket. The innkeeper at the Tabard advises telling a story to help pass the time.

Chaucer

Miller disagrees and begins a story about a bumbling carpenter, whereas the Knight began the first story with noble themes of love and knights. As retaliation, Reeve told a crass story about a liar named Miller. After reading The Reeve’s Tale, the Chef, Roger, promises to tell a more authentic story. The Man of Law then begins his account of what happened to Constancy. In response to Parson’s wonderful tale, the Host demands that he tell another. The Parson, however, politely rejects and reprimands the Host for swearing and making fun of him. The next storyteller is the Woman of Bath, who begins by arguing that the only way a monogamous relationship can survive is if one partner is dominant over the other.

The Friar and the Summoner have finished their mutually destructive tale telling. The Squire complies and begins a ghost story. Franklin, though, cuts him off to compliment the Squire on his eloquence and manners. After hearing the Physician’s explanation of a father and daughter’s terrible situation, the Host is stunned and turns to the Pardoner, hoping for a lighter tale.

After the Prioress’s sombre account of a minor martyr, the host comes up to Chaucer and asks for his advice on how to cheer everyone up. When Chaucer begins telling a tale about Sir Topas, the Host cuts him off, saying, “I’m sick of the clanging melodies,” and suggesting that he tell a brief narrative instead in English. In order to pass the time, Chaucer listens to Melibee’s boring story, which he was told by the Nun’s Priest. The Nun’s Priest tells the tale of Chaunticleer, his mistress, the fox, and the rooster from the barnyard. The Second Nun then proceeds to deliver a story suited for her station by relating events from the life of St. Cecilia. The final member of the group, the Parson, relates his story. After writing The Tales, Chaucer revises his earlier account of the sermon delivered by The Parson.

About the Author

Chaucer, Geoffrey, “the discoverer of our language,” was an early and renowned English poet who lived before Shakespeare. They call him the “father of English poetry” and “father of English literature.” The first author to be laid to rest in Poets’ Corner of Westminster Abbey, he was also the first.

Extra Information

• People are frequently judged by their status in society, and they work hard to become wealthy. 
• People disregard their morals and ideals to advance in their careers.

Conclusion

The Canterbury Tales has enthralled and entertained readers more than any other of Chaucer’s writings, supporting the use of Middle English in informal writing by bringing the characters and their stories to life. The Canterbury Tales would give Chaucer the distinction of being “The Father of English Literature” and immortalize him as the creator of one of the finest works ever written in English.

Textbook Questions and Answers

1. What is the goal of Chaucer’s Canterbury Tales to depict the seven deadly sins?

Ans: The Seven Deadly Sins are used to highlight the pilgrims’ hypocrisy in The Canterbury Tales. Saint Thomas Aquinas enlarged the Seven Deadly Sins in the thirteenth century after initially defining them in the sixth.

2. The Canterbury Tales were composed in what dialect?

Ans: Middle English, an ancestor of Modern English, is used in The Canterbury Tales. Old English, Germanic, and French were the languages that gave rise to Middle English, which was spoken from the Norman Conquest (1066) until the late 1400s. Some terms, like “ferne halwes,” which is typically rendered as “far shrines,” are completely foreign to Modern English.

3. What do the initial character portraits in Chaucer’s The Canterbury Tales Prologue imply?

Ans: Due to the Knight’s great status, Chaucer begins by describing him and his heir, the Squire. The Knight is referred to as “a prominent man” who has always acted honourably, generously, and with chivalry. He has frequently displayed bravery in conflict and received recognition for his efforts. Although he has numerous reasons to be proud, he never says anything “boorish,” remaining meek and courteous throughout. His attire, which is soiled and battle-worn rather than elegant and elaborate, represents his modest demeanour. 

Frequently Asked Questions

1. What is Middle English?

Ans: Middle English is the language spoken in England from the 12th to the 15th centuries. It is a form of Old English that was heavily influenced by French and Latin..

2. What is the Canterbury Tales?

Ans: The Canterbury Tales is a collection of stories written by Geoffrey Chaucer in the late 14th century. It is a collection of 24 stories told by a group of pilgrims on their way to the shrine of Thomas Becket in Canterbury.

3. How did Chaucer expose the personalities in his works and name the rhetorical technique in the Canterbury Tales?

Ans: By using specific descriptions, revealing comments, and the stories each traveller relates, Chaucer makes his characters transparent. Ten-syllabic is the rhetorical technique used in the Canterbury Tales Prologue.