Deck 32: Geometric Optics

Question 1

What is the speed of light in an optical fiber whose index of refraction is 1.265?

A)1.539 * 10⁸ m/s
B)1.828 * 10⁸ m/s
C)2.372 * 10⁸ m/s
D)2.651 * 10⁸ m/s

Answer 1

2.372 * 10⁸ m/s

Question 2

For a convex spherical mirror

A)the image is always virtual.
B)the radius of curvature is always negative.
C)the image is always upright.
D)All are correct.

Answer 2

All are correct.

Question 3

The the frequency and wavelength of light in an optical fiber are 4.57 * 10¹⁴ Hz and 437 nm,respectively.What is the index of refraction of the optical fiber?

A)1.27
B)1.61
C)1.42
D)0.666
E)1.50

Answer 3

1.50

Question 4

For a concave mirror,when is the object distance equal to the image distance?

A)when the magnification is equal to zero
B)when the radius of curvature is equal to the image distance
C)when the radius of curvature is equal to half the object distance
D)when the focal length is zero

Question 5

The the frequency and wavelength of light in an optical fiber are 4.57 *10¹⁴ Hz and 437 nm,respectively.What is the critical angle for light in this optical fiber,if the fiber is surrounded by water (n=1.33)?

A)57.9 ^$\circ$
B)62.3 ^$\circ$
C)48.8 ^$\circ$
D)41.7 ^$\circ$
E)65.4 ^$\circ$

Question 6

A person sits 2.0 m in front of a plane mirror.What is the location of the image?

A)2.0 m in front of the mirror
B)0.5 m in front of the mirror
C)2.0 m behind the mirror
D)0.5 m behind the mirror

Question 7

A beam of light enters a liquid solution from air at an angle of 35 ^$\circ$ with the normal to its surface.The refracted beam makes an angle of 24 ^$\circ$ to the normal of the liquid.What is the index of refraction for the liquid?

A)1.1
B)1.4
C)1.5
D)1.7
E)2.0

Question 8

For a concave spherical mirror

A)the image is always virtual.
B)the radius of curvature is always negative.
C)the image is always upright.
D)All are correct.
E)None are correct

Question 9

The critical angle for total internal reflection for light entering water (n = 1.33)from oil is 61 ^$\circ$ .What is the index of refraction of the oil?

A)1.52
B)1.39
C)1.14
D)1.61

Question 10

For a concave mirror,when is the object distance equal to the image distance?

A)when the magnification is equal to zero
B)when the focal length is equal to the image distance
C)when the focal length is equal to half the object distance
D)when the focal length is zero

Question 11

An optical fiber with index of refraction of 1.340 is surrounded by air.What is the critical angle for light to transport through this fiber without loss?

A)12.56 ^$\circ$
B)67.44 ^$\circ$
C)35.62 ^$\circ$
D)52.23 ^$\circ$
E)48.27 ^$\circ$

Question 12

Which kind of curved mirror never suffers from spherical aberration?

A)convex
B)concave
C)circular
D)None are correct.

Question 13

When light travels across the interface from a material with a higher index of refraction to a material with a lower index of refraction,which of the following statements is always true?

A)The light never bends away from the interface between the two materials.
B)The light never bends toward the interface between the two materials.
C)The light never travels in a straight line across the interface between the two materials.
D)The light never speeds up.

Question 14

A periscope consists of two flat mirrors and is used for viewing objects when an obstacle impedes the direct viewing.Suppose that Curios George is looking through a periscope at the man with the yellow hat whose hat is at d_o = 2.0 m from the upper mirror and that the two flat mirrors are separated by a distance L = 0.5 m.What is the distance D of the final image of the yellow hat from the lower mirror?

A)1.0 m
B)1.5 m
C)2.0 m
D)2.5 m
E)3.0 m

Question 15

What is the critical angle for total internal reflection for light entering air (n = 1.00)from water (n = 1.33)?

A)41.3 degrees
B)48.7 degrees
C)90.0 degrees
D)There is no such angle.

Question 16

At what angle with the normal to the surface of the water must a beam of light enter the water so that the refracted beam makes an angle of 10 ^$\circ$ to the normal of the water?

A)10 ^$\circ$
B)13 ^$\circ$
C)15 ^$\circ$
D)17 ^$\circ$
E)20 ^$\circ$

Question 17

The speed of light with wavelength 589.3 nm through an unknown uniform solid sample is 1.241 * 10⁸ m/s.Identify the solid.

A)fused quartz
B)typical glass
C)quartz
D)diamond

Question 18

A periscope consists of two flat mirrors and is used for viewing objects when an obstacle impedes the direct viewing.Suppose that Curios George is looking through a periscope at the man with the yellow hat whose hat is at d_o = 2.0 m from the upper mirror and that the two flat mirrors.If the image of the man is d_i = 2.75 m away from the lower mirror,what is the distance between the two mirrors?

A)0.75 m
B)1.15 m
C)0.50 m
D)1.5 m
E)4.75 m

Question 19

What is the critical angle for total internal reflection for light entering water (n = 1.33)from air (n = 1.00)?

A)41.3 degrees
B)48.7 degrees
C)90.0 degrees
D)There is no such angle.

Question 20

The speed of light in an optical fiber is 1.83 * 10⁸ m/s What is the index of refraction of the optical fiber?

A)0.610
B)1.27
C)1.52
D)1.64
E)5.49

Question 21

A metallic,spherical Christmas tree ornament has a diameter of 16.00 cm.If Saint Nicholas is by the fireplace,0.720 m away,where will he see his reflection relative to the surface of the ornament?

A)-7.2 cm
B)-3.8 cm
C)4.2 cm
D)9.0 cm
E)21 cm

Question 22

Convex mirrors are often used in side-view mirrors on trucks.Such mirrors often warn "Objects in mirror are closer than they appear." Assume a convex mirror has a radius of curvature of 12.0 m and that there is a car that is 14.0 m behind the mirror.Find the magnitude of the distance between the mirror and the image of the car.

A)4.2 m
B)6.5 m
C)10.5 m
D)14 m
E)16.2 m

Question 23

Standing by the pool filled with water,under what condition will you see the reflection of the scenery on the opposite side through total internal reflection of the image?

A)if you put your eyes level with the water
B)if you observe the pool at an angle of 41.8 degrees
C)under no condition
D)if you observe the pool at an angle of 48.2 degrees

Question 24

A collimated laser beam moves downward an angle 20.0 ^$\circ$ with respect to horizontal and strikes the left side of a ZnSe block.The block has an index of refraction of 2.44 and is surrounded by air with an index of 1.00.The left side of the glass block is vertical (90.0 ^$\circ$ from horizontal)while the right side of the block slopes upward at an angle of 75.0 ^$\circ$ from horizontal,i.e.,the block is thicker at the top than at the bottom.Determine the angle with respect to horizontal at which the light travels after it exits the right surface of the block.

A)2.2 ^$\circ$
B)0 ^$\circ$
C)17 ^$\circ$
D)8.1 ^$\circ$
E)15 ^$\circ$

Question 25

A real image of an object placed 10 cm from a concave spherical mirror is formed 30 cm from the mirror.What is the radius of curvature of the mirror?

A)10 cm
B)15 cm
C)20 cm
D)25 cm
E)30 cm

Question 26

A single concave spherical mirror is used to create an image of a 6.00-cm tall source.The source is located 23.0 cm to the left of the mirror's center of curvature.The magnitude of the radius of curvature for the mirror is 12.0 cm.Calculate the magnification.

A)+0.52
B)+0.35
C)-0.21
D)-0.35
E)-0.52

Question 27

A single convex spherical mirror is used to create an image of a 10.0-cm tall source that is located 35.0 cm to the left of the mirror.The magnitude of the radius of curvature for the mirror is 15.0 cm.Where does the image form?

A)6.2 cm to the left of the mirror
B)6.2 cm to the right of the mirror
C)26.2 cm to the left of the mirror
D)26.2 cm to the right of the mirror
E)35.4 cm to the right of the mirror

Question 28

Light hits the surface of water (n = 1.33)at an incident angle of 25.0 degrees with respect to the normal line.What is the angle between the reflected ray and the refracted ray?

A)18.5 degrees
B)43.5 degrees
C)83.5 degrees
D)96.5 degrees
E)136.5 degrees

Question 29

In figure shown,what is the smallest incident angle $\theta$ _i for the beam to undergo total internal reflection at surface S of prism having an index of refraction of 1.5?

A)56.1 ^$\circ$
B)33.9 ^$\circ$
C)50.9 ^$\circ$
D)39.1 ^$\circ$

Question 30

A single concave spherical mirror is used to create an image of a source.The source is located 23.0 cm to the left of the mirror's center of curvature.The magnitude of the radius of curvature for the mirror is 12.0 cm.If the image is 0.88 cm tall,what is the height of the source?

A)5.6 cm
B)7.1 cm
C)6.4 cm
D)6.8 cm
E)6.0 cm

Question 31

A coin rests at the bottom of a 2.00-m deep pool of water.The index of refraction for the water is 1.33.For someone looking directly down on the coin from above the water surface,the apparent distance from the surface of the water to the coin is

A)1.23 m.
B)1.37 m.
C)1.50 m.
D)2.00 m.
E)2.66 m.

Question 32

Which of these approaches will most effectively reduce spherical aberration in a mirror?

A)use a larger mirror
B)use only a single wavelength of light to form the image
C)block light at edges of mirror
D)block light at center of mirror

Question 33

A collimated laser beam moves upward an angle 20.0 ^$\circ$ with respect to horizontal and strikes the left side of a ZnSe block.The block has an index of refraction of 2.44 and is surrounded by air with an index of 1.00.The left side of the glass block is vertical (90.0 ^$\circ$ from horizontal)while the right side of the block slopes upward at an angle of 75.0 ^$\circ$ from horizontal,i.e.,the block is thicker at the top than at the bottom.Determine the angle with respect to horizontal at which the light travels after it exits the right surface of the block.

A)58 ^$\circ$
B)73 ^$\circ$
C)0 ^$\circ$
D)2.2 ^$\circ$
E)88 ^$\circ$

Question 34

Light is incident on a heavy glass slab of refractive index 1.6.The speed of light in the glass is

A)3.0 * 10⁸ m/s.
B)2.5 * 10⁸ m/s.
C)1.88 * 10⁸ m/s.
D)1.5 * 10^-8 m/s.

Question 35

A single concave spherical mirror is used to create an image of a 6.00-cm tall source.The source is located 23.0 cm to the left of the mirror's center of curvature.The magnitude of the radius of curvature for the mirror is 12.0 cm.What is the height of the image?

A)0.11 cm
B)1.0 cm
C)0.88 cm
D)2.0 cm
E)1.24 cm

Question 36

A green laser beam and a red laser beam are directed onto the surface of a pool of water at an angle of 28 ^$\circ$ to the normal.Which of the following are true?

A)The beams continue along their original paths.
B)Both beams are bent away from the normal,but the green beam is bent more.
C)Both beams are bent away from the normal,but the red beam is bent more.
D)Both beams are bent towards the normal,but the green beam is bent more.
E)Both beams are bent towards the normal,but the red beam is bent more.

Question 37

An optical fiber with an index of refraction of 1.5 is used to transport light of wavelength 400 nm.What is the critical angle for light to transport through this fiber without loss if the fiber is immersed in water?

A)30 ^$\circ$
B)40 ^$\circ$
C)50 ^$\circ$
D)60 ^$\circ$
E)70 ^$\circ$

Question 38

Which of the following interface combinations have the smallest critical angle?

A)light traveling from ice to diamond
B)light traveling from quartz to lucite
C)light traveling from diamond to glass
D)light traveling from Lucite to diamond
E)light traveling from Lucite to quartz

Question 39

Light from a green laser pointer (wavelength in air is 532 nm)travels into water (n = 1.33).What is the speed,wavelength,and frequency while the light is inside water.

A)Option A
B)Option B
C)Option C
D)Option D
E)Option E

Question 40

A single concave spherical mirror is used to create an image of a 6.00-cm tall source.The source is located 23.0 cm to the left of the mirror's center of curvature.The magnitude of the radius of curvature for the mirror is 12.0 cm.Where is the image located?

A)9.05 cm to the right of the mirror
B)7.24 cm to the left of the mirror
C)7.24 cm to the right of the mirror
D)18.3 cm to the right of the mirror
E)9.05 cm to the left of the mirror

Question 41

A concave spherical mirror has radius 25 cm.An object is placed at the mirror's center.Where is its image?

A)at the focal point
B)at the center of the mirror
C)at twice the focal length away from the mirror
D)A and B are correct.
E)B and C are correct.

Question 42

Which pair is exchanged in the reflection from a plane mirror? You may wish to draw a sketch in order to help you determine the proper answer.

A)right and left
B)up and down
C)front and back
D)None are correct.
E)More than one of these.

Question 43

A beam of light is incident at the polarizing angle on a hard glass plate of refractive index 1.6.The Brewster's angle of refraction is

A)58 ^$\circ$ .
B)32 ^$\circ$ .
C)29 ^$\circ$ .
D)18 ^$\circ$ .

Question 44

A concave mirror has a radius of curvature of 30 cm.An object is located 45 cm in front of the mirror.Where is the image formed,and what are its properties?

A)The image is located at 22.5 cm in front of the mirror and is erect.
B)The image is located at 22.5 cm behind the mirror and is erect.
C)The image is located at 22.5 cm in front of the mirror and is inverted.
D)The image is located at 22.5 cm behind the mirror and is inverted.
E)No image is formed in this case.

Question 45

A ray of light in air with a wavelength of 600 nm is incident on a liquid with an index of refraction of 1.5.The ray of light makes an angle of 45 degrees with the normal when it enters the liquid.What is the wavelength of the ray of light in the liquid?

A)280 nm
B)400 nm
C)600 nm
D)900 nm
E)1300 nm

Question 46

The figure shows the boundary between two transparent materials with indexes of refraction n₁ and n₂.Ray A is found to suffer total internal reflection.Which one statement is correct?

A)n₂ > n₁
B)Rays B and D must also suffer total internal reflection.
C)Ray E must be totally internally reflected.
D)Ray B may be totally internally reflected.
E)Ray C may be totally internally reflected.

Question 47

An object is placed 40 cm from a concave mirror with radius of curvature 50 cm.The image will be

A)real,upright,and enlarged.
B)real,upright,and diminished.
C)real,inverted,and enlarged.
D)real,inverted,and diminished.
E)None are correct.

Question 48

If n₁ = 1.3 and n₂ = 2.2,what is the condition for the angle $\theta$ for no light escaping?

A) $\theta$ > 54 ^$\circ$
B) $\theta$ < 54 ^$\circ$
C) $\theta$ > 36 ^$\circ$
D) $\theta$ < 36 ^$\circ$
E)Light escapes for all $\theta$ .

Question 49

An object is 50 cm from a concave mirror.The size of the real image is ½ the size of the object.The radius of curvature of the mirror is

A)12.9 cm.
B)16.7 cm.
C)25.0 cm.
D)33.3 cm.

Question 50

Light passing through water (n = 1.33)in an aquarium is incident upon the heavy glass tank wall (n = 1.625)and is partially reflected.At what angle of incidence is the reflected light fully polarized?

A)55 ^$\circ$
B)39 ^$\circ$
C)51 ^$\circ$
D)35 ^$\circ$

Question 51

A beam of light is incident at the polarizing angle on a glass plate.If Brewster's angle is 55.4 ^$\circ$ what is the index of refraction of the glass?

A)1.55
B)1.60
C)1.50
D)1.40
E)1.45

Question 52

A ray of light is incident on an equilateral triangular prism with an index of refraction of 1.23.The ray is parallel to the base of the prism when before it enters the prism as shown in the figure.What is the angle of the ray relative to the normal when it emerges from the triangular prism? (Assume that the ray does not exit from the base.)

A)24 ^$\circ$
B)30 ^$\circ$
C)46 ^$\circ$
D)54 ^$\circ$
E)62 ^$\circ$

Question 53

Unpolarized light in air is reflected from a piece of flat glass at an angle of 58 ^$\circ$ with respect to the normal.The reflected light is found to be completely polarized after the reflection.What is the index of refraction of the glass?

A)1.2
B)1.3
C)1.4
D)1.6
E)1.9

Question 54

A fiber optic cable consists of a glass core surrounded by a layer of material called the cladding further surrounded by a protective cover as shown in the drawing above.If the index of refraction of the core is n1 = 1.50 and the index of refraction of the cladding is n2 = 1.20,what is the critical angle (in degrees)for total internal reflection for light traveling in the core?

A)17.0
B)22.6
C)30.0
D)39.9
E)53.1

Question 55

A cladded optical fiber for transmitting red light is constructed by placing a cladding material around a round plastic optical fiber.If the index of refraction of the plastic fiber core is 1.6 and the index of refraction of the cladding is 1.2,what is the critical angle for light to transport through the plastic fiber core without loss?

A)34 ^$\circ$
B)39 ^$\circ$
C)41 ^$\circ$
D)49 ^$\circ$
E)56 ^$\circ$

Question 56

An incident ray makes an angle of 30 ^$\circ$ with the horizontal in air as it hits a piece of glass with an index of refraction n_glass = 1.52.How much does the ray deviate from its path inside the glass?

A)10.5 ^$\circ$
B)25.3 ^$\circ$
C)14.7 ^$\circ$
D)45.2 ^$\circ$
E)0 ^$\circ$

Question 57

What kind of images,virtual or real,are formed by a converging mirror when the object for the mirror is placed a distance away from the mirror that is between the center of curvature of the mirror and a distance away that is half of the center of curvature of the mirror?

A)real images
B)virtual images
C)The answer cannot be determined without knowing the height of the object.

Question 58

Where must an object be placed in front of a concave mirror so that the image and object are the same size (F is the focal point and C is the center of curvature)?

A)at F
B)at C
C)between F and C
D)beyond C
E)between F and the mirror

Question 59

Which of the following statements is incorrect?

A)A convex mirror never forms a real image of a real object.
B)The image produced by a convex mirror is always closer to the mirror than it would be in a plane mirror for the same object distance.
C)The virtual image formed by a convex mirror is always enlarged.
D)When an object is placed between a concave mirror and its focal point,the image is virtual.

Question 60

An object is placed at half the focal length f away from a concave spherical mirror.Where is the image?

A)at f in front of the mirror
B)at f behind the mirror
C)at f/2 in front of the mirror
D)at f/2 behind the mirror
E)at 2f in front of the mirror

Question 61

Light with a frequency of 6 * 10¹⁶ Hz is traveling in a material with index of refraction n = 1.5.What is its wavelength in this material?

A)1.0 nm
B)2.0 nm
C)2.5 nm
D)3.3 nm
E)4.0 nm

Question 62

An object is located 40 cm in front of a concave mirror of focal length 12.5 cm.Where is the image located?

A)12.5 cm
B)10.5 cm
C)20.0 cm
D)29.1 cm
E)18.2 cm

Question 63

Particular glass has an index of refraction of 1.650 for blue light of wavelength 430 nm and 1.615 for red light of wavelength 680 nm.Consider a beam containing these two colors incident on this piece of glass,at an angle of 30 degrees from the normal.What is the angle between the red and the blue beam in the glass?

A)0 degrees
B)0.4 degrees
C)1.6 degrees
D)3.14 degrees
E)9.6 degrees