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Elements of Physics for Students of Science and Engineering

George Hiram Shortley

Chapter 23

REFRACTION OF LIGHT - all with Video Answers

Educators


Chapter Questions

01:25

Problem 1

A ray of light in air strikes a water surface at an angle of incidence of $30^{\circ}$. What is the angle of refraction? Show diagram.

Kristela Garcia
Kristela Garcia
Numerade Educator
04:04

Problem 2

A ray of light in air strikes the surface of a diamond at an angle of incidence of $30^{\circ}$. What is the angle of refraction? Show diagram.

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00000 00000
Numerade Educator
00:54

Problem 3

. The index of refraction of a certain type of glass is 1.52. Taking $c=3 \times$ $10^8 \mathrm{~m} / \mathrm{sec}$, calculate the speed of light in this glass.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:02

Problem 4

What is the speed of light in water? in diamond?

Narayan Hari
Narayan Hari
Numerade Educator
02:21

Problem 5

A shallow tank with a flat glass bottom contains carbon disulfide. A ray of light in air is incident at the surface of the carbon disulfide at an angle of $45^{\circ}$. If the refractive index of the glass is 1.517 , find the angle of refraction of the light inside the glass. Show diagram.

Adnan Gill
Adnan Gill
Numerade Educator
02:15

Problem 6

If the tank described in Prob. 5 were filled with water instead of carbon disulfide, what would be the angle of refraction of the light ray inside the glass? Show that an empty tank would give the same angle.

Samantha Baker
Samantha Baker
Numerade Educator
03:20

Problem 7

A ray of light in air has an angle of incidence of $30^{\circ}$ at the surface of a plate of glass 4.0 cm thick, with $\mu=1.523$. The ray emerging from the glass is parallel to the incident ray but is displaced laterally with respect to the incident ray. What is the magnitude of the lateral displacement?

Shoukat Ali
Shoukat Ali
Other Schools
03:14

Problem 8

A stick 4 ft long, marked off in feet, is placed vertically at the shallow end of a swimming pool, where the water is 3 ft deep. The $1-\mathrm{ft}$ mark is at the surface of the water, the 4 -ft mark at the bottom. An observer stands at the opposite end of the pool with his eyes 20 ft horizontally from the stick and 7 ft above the water surface. What is the apparent depth of the 2 -, 3 -, and 4 - ft marks below the surface, as the observer would judge by comparison with the distance from the top of the stick to the 1-ft mark?

Satpal Satpal
Satpal Satpal
Numerade Educator
01:29

Problem 9

An observer looks from directly above at a small stone at the bottom of a pool of water. The stone appears to be 3 ft beneath the surface of the water. What is the actual depth of the pool?

Zhaojie Xu
Zhaojie Xu
Numerade Educator
02:25

Problem 10

A ray of light in water strikes the horizontal surface of the water at angle of incidence of $30^{\circ}$. What is the angle of refraction in air? What is the angle of incidence in water when the angle of refraction in air is $90^{\circ}$ ? Show diagrams. What is the critical angle for water?

Konstantin Pavlovskii
Konstantin Pavlovskii
Numerade Educator
01:23

Problem 11

What is the angle of deviation $D$ when yellow light is incident at an angle of $50^{\circ}$ on the dense flintglass prism in Fig. 23?

Suzanne W.
Suzanne W.
Numerade Educator
01:23

Problem 12

What is the angle of deviation $D$ when yellow light is incident at an angle of $70^{\circ}$ on the dense flintglass prism in Fig. 23?

Suzanne W.
Suzanne W.
Numerade Educator
01:05

Problem 13

Neglecting the curvature of the earth, compute the deviation of starlight incident at an angle of $80^{\circ}$ (the star is $10^{\circ}$ above the horizon) on the top of the earth's atmosphere if the index of refraction of the air at the earth's surface is 1.00030 .

Raj Bala
Raj Bala
Numerade Educator
01:15

Problem 14

The index of refraction of air depends only on temperature, pressure, and humidity. An astronomer reads temperature, pressure, and humidity at the earth's surface, and measures the apparent angle of a star from the zenith. He then looks up in a table the correction to be applied to give the true angle. To the approximation in which the curvature of the earth can be neglected and in which the atmosphere can be assumed to have characteristics that vary with altitude but do not vary in any given horizontal plane, show that these tables can be rigorously compiled because the angle of deviation depends only on the index of refraction at the earth's surface and is independent of the manner in which this index varies as one ascends to the top of the atmosphere.

Farhanul Hasan
Farhanul Hasan
Numerade Educator
02:47

Problem 15

Why do stars twinkle? Why does the air over a hot radiator seem to shimmer?

Ashok Prajapati
Ashok Prajapati
Numerade Educator
01:18

Problem 16

What is the minimum index of refraction glass can have and still give total reflection for the light paths shown through the $90^{\circ}$ prism of Fig. 4(c)?

Suzanne W.
Suzanne W.
Numerade Educator
01:18

Problem 17

What is the minimum index of refraction glass can have and still give total reflection in the case of the $90^{\circ}$ prisms shown in (a) and (b) of Fig. 4? Ans: 1.414.

Suzanne W.
Suzanne W.
Numerade Educator
01:53

Problem 18

What is the critical angle for diamond? Explain how the high index of refraction of diamond accounts for its extraordinary 'sparkle' when cut as a gem.

Satpal Satpal
Satpal Satpal
Numerade Educator
01:58

Problem 19

A large slab of glass of index 1.650 has a small air bubble a short distance below the surface. A dime (diameter 1.75 cm ) placed on the surface of the glass is just large enough to completely prevent the bubble from being seen through the surface. How far down is the air bubble?

Keshav Singh
Keshav Singh
Numerade Educator
04:57

Problem 20

Why is a camera lens with a $180^{\circ}$ field of view called a 'fish-eye lens'? What is the angle of the cone in which a fish would see the whole of the world above the level surface of a fresh-water lake?

Vipender Rao
Vipender Rao
Numerade Educator
01:33

Problem 21

A double-convex lens of crown glass has surfaces with radii of curvature of 40 cm and 50 cm , respectively. What is its focal length?

Carlos Henrique De Lima
Carlos Henrique De Lima
Numerade Educator
01:16

Problem 22

What should be the radius of curvature of the curved surface of a planoconvex crown-glass lens if the lens is to have a focal length of 20 cm ?

Carlos Henrique De Lima
Carlos Henrique De Lima
Numerade Educator
02:34

Problem 23

An object 4 cm tall is placed near the axis of a thin converging lens at a distance of 33.3 cm from the lens. If the focal length of the lens is 20 cm , where will the image be formed and what will be the size of the image? Sketch the principalray diagram.

Arun Bana
Arun Bana
Numerade Educator
04:14

Problem 24

An object 2 cm tall is placed 10 cm from a diverging lens of $-10-\mathrm{cm}$ focal length. Where will the image be formed? What will be the size of the image? Sketch the principal-ray diagram.

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00000 00000
Numerade Educator
05:58

Problem 25

A converging lens has a focal length of 10 cm . Determine the image distances when an object is placed at the following distances from the lens: 25 cm , $20 \mathrm{~cm}, 15 \mathrm{~cm}, 10 \mathrm{~cm}$, and 5 cm .

William Dunkerton
William Dunkerton
Numerade Educator
05:37

Problem 26

A diverging lens has a focal length of -10 cm . Locate the images produced when an object is placed at the following distances from the lens: 25 cm , $20 \mathrm{~cm}, 15 \mathrm{~cm}, 10 \mathrm{~cm}$, and 5 cm .

William Dunkerton
William Dunkerton
Numerade Educator
01:15

Problem 27

An image of the sun is formed by a converging lens of $2-\mathrm{m}$ focal length. The sun's angular diameter is $32^{\prime}$ of are. What is the diameter of the image? Sketch the principal-ray diagram.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:16

Problem 28

Two distant stars are imaged on a photographic plate by a converging telescope lens of $8-\mathrm{m}$ focal length. The distance between the images is 1 mm . What is the angular separation of the stars in the sky?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:30

Problem 29

A concavo-convex spectacle lens has a power of +2 diopters. If the glass has a refractive index of 1.6 and the concave surface a radius of -1 m , what is the radius of the convex surface?

Narayan Hari
Narayan Hari
Numerade Educator
01:22

Problem 30

Why does a piece of glass of irregular shape become invisible when it is immersed in a liquid of the same index of refraction?

Abhishek Kumar
Abhishek Kumar
Numerade Educator
02:00

Problem 31

A converging lens of $10-\mathrm{cm}$ focal length is made of glass of refractive index 1.523. What is its focal length when immersed in water?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:25

Problem 32

Insert a pencil through a water surface at an angle of $45^{\circ}$, and observe that the pencil appears to be bent through a certain angle at the point where it enters the water. Compute this angle of bend for the case where your line of sight to the point of entry is at $45^{\circ}$ to the water surface, and the vertical plane containing the pencil is perpendicular to the vertical plane containing the line of sight.

Kajal Gautam
Kajal Gautam
Numerade Educator
05:42

Problem 33

Two converging lenses are placed 10 cm apart. The focal length of the first lens is 20 cm and that of the second is 30 cm . If an object is placed 40 cm in front of the first lens, where will the final image be formed? Sketch the principalray diagram.

Zachary Warner
Zachary Warner
Numerade Educator
02:58

Problem 34

A converging lens of focal length 10 cm is placed 20 cm in front of a diverging lens of focal length -10 cm . If an object is placed 40 cm in front of the converging lens, where will the final image be formed?

Mayukh Banik
Mayukh Banik
Numerade Educator
01:02

Problem 35

Two converging lenses of focal lengths 40 and 50 cm are placed in contact. What is the focal length of this lens combination? What is the power of the combination in diopters?

Suzanne W.
Suzanne W.
Numerade Educator
01:02

Problem 36

. A 4-diopter converging lens and a 2-diopter diverging lens are placed in contact. What is the focal length of the resulting compound lens?

Suzanne W.
Suzanne W.
Numerade Educator
02:19

Problem 37

A converging lens of focal length 20 cm is placed in front of a converging lens of focal length 4 cm . What is the distance between the lenses if parallel rays entering the first lens leave the second lens as parallel rays? Ans: 24 cm .

Nathan Silvano
Nathan Silvano
Numerade Educator
02:37

Problem 38

A converging lens of focal length 50 cm is placed in front of a diverging lens of focal length -5 cm . What is the distance between the lenses if parallel rays entering the first lens leave the second lens as parallel rays?

Sarah Mccrumb
Sarah Mccrumb
Numerade Educator
05:22

Problem 39

An object is placed 8 cm in front of a diverging lens of focal length -8 cm . A converging lens of focal length 15 cm is placed behind the diverging lens and forms a final image at infinity. What is the distance between the lenses? Sketch the principal-ray diagram.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:58

Problem 40

An object is placed 16 cm in front of a converging lens of focal length 8 cm . A diverging lens of focal length -12 cm is placed behind the converging lens and forms a final image at infinity. What is the distance between the lenses? Sketch the principal-ray diagram.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:55

Problem 41

. An object is placed 8 cm in front of a converging lens of focal length 8 cm . A diverging lens of focal length -12 cm is placed 4 cm behind the converging lens. Find the position, size, and character of the final image.

Sean Dougherty
Sean Dougherty
Numerade Educator
02:55

Problem 42

. An object is placed 8 cm in front of a converging lens of focal length 8 cm . A converging lens of focal length 12 cm is placed 4 cm behind the first lens. Find the position, size and character of the final image.

Sean Dougherty
Sean Dougherty
Numerade Educator
06:21

Problem 43

A converging lens of focal length 20 cm is placed 20 cm from a diverging mirror of focal length -10 cm . A candle is midway between the lens and the mirror. Where should a screen be placed to catch a real image of the candle flame? What is the image size? Is the image erect or inverted?

Vishal Gupta
Vishal Gupta
Numerade Educator
05:22

Problem 44

A converging lens of focal length 20 in is placed 20 in from a converging mirror of focal length 4 in . A candle is placed midway between the lens and the mirror. Describe the two images of the candle flame (position, size, character) seen when one looks through the lens. Sketch the principal-ray diagram.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
05:43

Problem 45

By the method used on p. 473 to derive the lens equation from the prin-ciple-ray diagram of Fig. 13 in the case of formation of a real image by a converging lens, derive the same equation for the following cases, using the sign conventions given at the top of p. 476:
(a) The formation of a virtual image by a converging lens, as in Fig. 14.
(b) The formation of a virtual image by a diverging lens, as in Fig. 18.
(c) The formation of the image of a virtual object by a converging lens, as in the case of lens $L_2$ in Fig. 21.
(d) The formation of a real image of a virtual object by a diverging lens.
(e) The formation of a virtual image of a virtual object by a diverging lens.

Carlos Henrique De Lima
Carlos Henrique De Lima
Numerade Educator