Question 1

A object is 12 cm in front of a concave spherical mirror, and the image is 3.0 cm in front of the mirror. What is the focal length of the mirror?

Accepted Answer

A)  0.25 cm 
B)  15 cm 
C)  4.0 cm 
D)  2.4 cm 
E)  1.3 cm 
A)  0.25 cm 
B)  15 cm 
C)  4.0 cm 
D)  2.4 cm 
E)  1.3 cm

Question 2

The objective lens of a refracting telescope has a focal length of 60 cm and the eyepiece a focal length of 8.0 cm. What is the angular magnification of the telescope?

Accepted Answer

A)  34 x 
B)  480 x 
C)  68 x 
D)  0.13 x 
E)  7.5 x 
A)  34 x 
B)  480 x 
C)  68 x 
D)  0.13 x 
E)  7.5 x

Question 3

A convex-concave thin lens is made with the radius of curvature of the convex surface being 25.0 cm and the concave surface 45.0 cm. If the glass used has index of refraction 1.500, what is the focal length of this lens?

Accepted Answer

A)  -32.0 cm 
B)  32.0 cm 
C)  113 cm 
D)  67.5 cm 
E)  -113 cm 
A)  -32.0 cm 
B)  32.0 cm 
C)  113 cm 
D)  67.5 cm 
E)  -113 cm

Question 4

The focal lengths of the objective and the eyepiece in a microscope are 0.29 cm and 2.50 cm, respectively. An object is placed at 0.30 cm from the objective lens and the image of this object is viewed with the eyepiece adjusted for minimum eyestrain (with the eye focused at the far point). The near point of the person using the microscope is 25 cm and the far point is at infinity. What is the final overall magnification of the microscope?

Accepted Answer

A)  -190 x 
B)  -240 x 
C)  -300 x 
D)  -320 x 
E)  -470 x 
A)  -190 x 
B)  -240 x 
C)  -300 x 
D)  -320 x 
E)  -470 x

Question 5

What is the focal length of a magnifying glass that produces an angular magnification of 7.0 x when used by a person with a near point at 28 cm?

Accepted Answer

A)  2.0 cm 
B)  3.0 cm 
C)  4.0 cm 
D)  5.0 cm 
E)  6.0 cm 
A)  2.0 cm 
B)  3.0 cm 
C)  4.0 cm 
D)  5.0 cm 
E)  6.0 cm

Question 6

In the figure, the radius of curvature of the curved part of the lens is 35.0 cm, and the refractive index of the lens material is 1.620. What is the focal length of the lens?

Accepted Answer

A)  +56.5 cm 
B)  -56.5 cm 
C)  +28.2 cm 
D)  +21.6 cm 
E)  -21.6 cm 
A)  +56.5 cm 
B)  -56.5 cm 
C)  +28.2 cm 
D)  +21.6 cm 
E)  -21.6 cm

Question 7

An object 1.80 cm tall is placed 100 cm in front of a diverging lens having a focal length of magnitude 25 cm. A converging lens with a focal length of magnitude 33.33 cm is placed 30 cm past the first lens. What is the lateral magnification of this system of lenses?

Accepted Answer

A)  2.5 
B)  -2.5 
C)  -0.40 
D)  1.0 
E)  0.40 
A)  2.5 
B)  -2.5 
C)  -0.40 
D)  1.0 
E)  0.40

Question 8

The image of a plant is 4.0 cm from a concave spherical mirror having a radius of curvature of 10 cm. Where is the plant relative to the mirror?

Accepted Answer

A)  2.2 cm in front of the mirror 
B)  4.4 cm in front of the mirror 
C)  9.0 cm in front of the mirror 
D)  1.0 cm in front of the mirror 
E)  20 cm in front of the mirror 
A)  2.2 cm in front of the mirror 
B)  4.4 cm in front of the mirror 
C)  9.0 cm in front of the mirror 
D)  1.0 cm in front of the mirror 
E)  20 cm in front of the mirror

Question 9

A compound lens is made by joining the plane surfaces of two thin plano-convex lenses of different glasses. The radius of curvature of each convex surface is 80 cm. The indices of refraction of the two glasses are 1.50 and 1.60. What is the focal length of the compound lens?

Accepted Answer

A)  67 
B)  69 
C)  71 
D)  73 
E)  75 
A)  67 
B)  69 
C)  71 
D)  73 
E)  75

Question 10

An object 3.4 mm tall is placed 25 cm from the vertex of a convex spherical mirror. The radius of curvature of the mirror has a magnitude of 52 cm.
(a) How far is the image from the vertex of the mirror?
(b) What is the height of the image?

Accepted Answer

(a) 13 cm

Question 11

A machinist with normal vision has a near point at 25 cm. The machinist wears eyeglasses in order to do close work. The power of the lenses is +1.75 diopters. With these eyeglasses, what is the near point of the machinist?

Accepted Answer

A)  17 cm 
B)  14 cm 
C)  10 cm 
D)  21 cm 
E)  24 cm 
A)  17 cm 
B)  14 cm 
C)  10 cm 
D)  21 cm 
E)  24 cm

Question 12

The focal lengths of the objective and the eyepiece in a microscope are 0.290 cm and 2.50 cm, respectively. An object is placed 0.300 cm from the objective. The image of this object is viewed with the eyepiece adjusted for minimum eyestrain (image at the far point of the eye) for a person with normal vision. What is the distance between the objective and the eyepiece?

Accepted Answer

A)  9.85 cm 
B)  10.1 cm 
C)  10.4 cm 
D)  11.2 cm 
E)  11.5 cm 
A)  9.85 cm 
B)  10.1 cm 
C)  10.4 cm 
D)  11.2 cm 
E)  11.5 cm

Question 13

It is desired to project the image of an object four times its actual size using a lens of focal length 20 cm. How far from the lens should the object be placed?

Accepted Answer

A)  100 cm 
B)  80 cm 
C)  4.0 cm 
D)  25 cm 
E)  5.0 cm 
A)  100 cm 
B)  80 cm 
C)  4.0 cm 
D)  25 cm 
E)  5.0 cm

Question 14

A double-convex thin lens is made of glass with an index of refraction of 1.52. The radii of curvature of the faces of the lens are 60 cm and 72 cm. What is the focal length of the lens?

Accepted Answer

A)  70 cm 
B)  63 cm 
C)  75 cm 
D)  66 cm 
E)  58 cm 
A)  70 cm 
B)  63 cm 
C)  75 cm 
D)  66 cm 
E)  58 cm

Question 15

A man is nearsighted and cannot see things clearly beyond 110from his eyes. What is the focal length of the contact lenses that will enable him to see very distant objects clearly?

Accepted Answer

A)  50 cm 
B)  -50 cm 
C)  -110 cm 
D)  110 cm 
E)  -30 cm 
A)  50 cm 
B)  -50 cm 
C)  -110 cm 
D)  110 cm 
E)  -30 cm

Question 16

A man's face is 30 cm in front of a concave spherical shaving mirror. If the image is erect and 1.5 times as large as his face, what is the radius of curvature of the mirror?

Accepted Answer

A)  40 cm 
B)  60 cm 
C)  100 cm 
D)  140 cm 
E)  180 cm 
A)  40 cm 
B)  60 cm 
C)  100 cm 
D)  140 cm 
E)  180 cm

Question 17

As you walk away from a vertical plane mirror, your image in the mirror

Accepted Answer

A)  is always the same height. 
B)  may or may not decrease in height, depending on where the observer is positioned. 
C)  is always a real image, no matter how far you are from the mirror. 
D)  changes from being a virtual image to a real image as you pass the focal point. 
E)  decreases in height. 
A)  is always the same height. 
B)  may or may not decrease in height, depending on where the observer is positioned. 
C)  is always a real image, no matter how far you are from the mirror. 
D)  changes from being a virtual image to a real image as you pass the focal point. 
E)  decreases in height.

Question 18

What is the angular magnification of a magnifying glass of focal length 4.0 cm if the image is to be viewed by a relaxed eye (image at the far point) having a near point of 25 cm and a far point at infinity?

Accepted Answer

A)  2.0 x 
B)  3.0 x 
C)  3.6 x 
D)  4.0 x 
E)  6.3 x 
A)  2.0 x 
B)  3.0 x 
C)  3.6 x 
D)  4.0 x 
E)  6.3 x

Question 19

A convex spherical mirror with a focal length of magnitude 25 cm has a 4.0-cm tall flower placed 100 cm in front of it. What is the height of the image of the flower?

Accepted Answer

A)  0.80 cm 
B)  20 cm 
C)  4.0 cm 
D)  1.6 cm 
E)  8.0 cm 
A)  0.80 cm 
B)  20 cm 
C)  4.0 cm 
D)  1.6 cm 
E)  8.0 cm

Question 20

A double-concave lens has equal radii of curvature of 15.1 cm. An object placed 14.2 cm from the lens forms a virtual image 5.29 cm from the lens. What is the index of refraction of the lens material?

Accepted Answer

A)  1.90 
B)  1.98 
C)  1.82 
D)  1.77 
A)  1.90 
B)  1.98 
C)  1.82 
D)  1.77

Exam 33: Geometric Optics

A object is 12 cm in front of a concave spherical mirror, and the image is 3.0 cm in front of the mirror. What is the focal length of the mirror?

The objective lens of a refracting telescope has a focal length of 60 cm and the eyepiece a focal length of 8.0 cm. What is the angular magnification of the telescope?

A convex-concave thin lens is made with the radius of curvature of the convex surface being 25.0 cm and the concave surface 45.0 cm. If the glass used has index of refraction 1.500, what is the focal length of this lens?

What is the focal length of a magnifying glass that produces an angular magnification of 7.0 x when used by a person with a near point at 28 cm?

In the figure, the radius of curvature of the curved part of the lens is 35.0 cm, and the refractive index of the lens material is 1.620. What is the focal length of the lens?

An object 1.80 cm tall is placed 100 cm in front of a diverging lens having a focal length of magnitude 25 cm. A converging lens with a focal length of magnitude 33.33 cm is placed 30 cm past the first lens. What is the lateral magnification of this system of lenses?

The image of a plant is 4.0 cm from a concave spherical mirror having a radius of curvature of 10 cm. Where is the plant relative to the mirror?

A compound lens is made by joining the plane surfaces of two thin plano-convex lenses of different glasses. The radius of curvature of each convex surface is 80 cm. The indices of refraction of the two glasses are 1.50 and 1.60. What is the focal length of the compound lens?

An object 3.4 mm tall is placed 25 cm from the vertex of a convex spherical mirror. The radius of curvature of the mirror has a magnitude of 52 cm. (a) How far is the image from the vertex of the mirror? (b) What is the height of the image?

A machinist with normal vision has a near point at 25 cm. The machinist wears eyeglasses in order to do close work. The power of the lenses is +1.75 diopters. With these eyeglasses, what is the near point of the machinist?

It is desired to project the image of an object four times its actual size using a lens of focal length 20 cm. How far from the lens should the object be placed?

A double-convex thin lens is made of glass with an index of refraction of 1.52. The radii of curvature of the faces of the lens are 60 cm and 72 cm. What is the focal length of the lens?

A man is nearsighted and cannot see things clearly beyond 110from his eyes. What is the focal length of the contact lenses that will enable him to see very distant objects clearly?

A man's face is 30 cm in front of a concave spherical shaving mirror. If the image is erect and 1.5 times as large as his face, what is the radius of curvature of the mirror?

As you walk away from a vertical plane mirror, your image in the mirror

What is the angular magnification of a magnifying glass of focal length 4.0 cm if the image is to be viewed by a relaxed eye (image at the far point) having a near point of 25 cm and a far point at infinity?

A convex spherical mirror with a focal length of magnitude 25 cm has a 4.0-cm tall flower placed 100 cm in front of it. What is the height of the image of the flower?

A double-concave lens has equal radii of curvature of 15.1 cm. An object placed 14.2 cm from the lens forms a virtual image 5.29 cm from the lens. What is the index of refraction of the lens material?

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