Deck 23: Mirrors and Lenses

Question 1

In using ray tracing to graphically locate the image of an object that is placed in front of a mirror, describe three simple rays that you could draw that pass by the head of the object.

Answer 1

Ray 1: the radial ray; i.e., the ray drawn toward the center of curvature, which is then reflected back along the same path.
Ray 2: the parallel ray; i.e., the incoming ray parallel to the main axis, which is then reflected along a path that extends to the focal point.
Ray 3: the focal ray; i.e., the ray drawn toward the focal point, which is then reflected back parallel to the main axis.

Question 2

How does the thickness of a lens relate to it being converging or diverging?

Answer 2

A converging lens is thicker at its center than it is at its edges and a diverging lens is thinner at its center than it is at its edges.

Question 3

Consider a converging lens forming an image on a screen. What property of the image would be affected by covering the top half of the lens?

Answer 3

It would be half as bright since half of the light gets through the lens.

Question 4

In using ray tracing to graphically locate the image of an object that is placed in front of a lens, describe three simple rays that you could draw that pass by the head of the object.

Question 5

Take the lens maker equation and show that a lens which has been turned around (surface 1 becomes 2 and 2 becomes 1) has the same focal length.

Question 6

Why do large aperture telescopes use a mirror instead of a lens to focus light?

Question 7

Is it possible to see a virtual image?

A) yes, but only indirectly in the sense that if the virtual image is formed on a sheet of photographic film, one could later look at the picture formed
B) no, since the rays that seem to emanate from a virtual image do not in fact emanate from the image
C) no, since virtual images do not really exist
D) yes, since the rays that appear to emanate from a virtual image can be focused on the retina just like those from an illuminated object
E) yes, since almost everything we see is virtual because most things do not themselves give off light, but only reflect light coming from some other source

Question 8

The radius of curvature for a plane (flat) mirror is

A) zero.
B) negative.
C) infinite.
D) imaginary.

Question 9

The IMAGE of a plane mirror (of a real object) has the following characteristics:

A) real, erect, and magnification = 1
B) virtual, inverted, and magnification > 1
C) virtual, erect, and magnification = 1
D) real, inverted, and magnification < 1

Question 10

An object is placed a distance d in front of a plane mirror. The size of the image will be

A) the same size as the object, independent of the distance d or the position of the observer.
B) half as big as the size of the object.
C) dependent on the distance d.
D) twice the size of the object.
E) dependent on where you are positioned when you look at the image.

Question 11

You may have seen ambulances on the street with the letters of the word AMBULANCE written on the front of them, in such a way as to appear correctly when viewed in your car's rear-view mirror.

See Figure 23-1. How do the letters appear when you look directly at the ambulance?

A) a
B) b
C) c
D) d
E) e

Question 12

Suppose a lighted candle is placed a short distance from a plane mirror, as shown in Figure 23-2.

Where will the image of the flame be located?

A) at A
B) at B
C) at C
D) at M (at the mirror)

Question 13

At which, if any, of the points indicated in Figure 23-3 should you place your eye if you wish to see an image of the arrow in the mirror?

A) A
B) B
C) C
D) D

Question 14

In air a concave mirror has a focal length of 30. cm. Under water that same mirror would have ________ focal length.

A) a smaller
B) a larger
C) the same

Question 15

A "parallel ray" is a ray parallel to the

A) object axis
B) chief ray
C) optic axis
D) mirror radius

Question 16

The magnification M = -di/do is the ratio of image to object

A) angular size.
B) focal distances.
C) distance.
D) heights.

Question 17

The rear-view mirrors on the passenger side of many new cars have a warning written on them: "OBJECTS IN MIRROR ARE CLOSER THAN THEY APPEAR." This implies that the mirror must be

A) concave.
B) transparent.
C) plane.
D) convex.

Question 18

Two parallel rays (also parallel to the optic axis) reflect from a concave mirror. They intersect at

A) the center of curvature.
B) a point behind the mirror.
C) infinity.
D) the focal point.

Question 19

Given a concave mirror, rays of light originating from the center of curvature reflect off the mirror and focus at

A) infinity.
B) the center of curvature.
C) 2 R from the mirror.
D) the focal point.

Question 20

Consider a converging lens. If the object is inside the focal point, then the image will always be

A) at the focal point.
B) real.
C) virtual.
D) at infinity.

Question 21

If you stand in front of a concave mirror, exactly at its center of curvature,

A) you will see your image and you will appear smaller.
B) you won't see your image because it's focused at a different distance.
C) you will see your image at your same height; however it will be inverted.
D) you will see your image and you will appear larger.
E) you won't see your image because there is none.

Question 22

If you stand in front of a convex mirror, at the same distance from it as its radius of curvature,

A) you won't see your image because there is none.
B) you will see your image and you will appear larger.
C) you will see your image and you will appear smaller.
D) you won't see your image because it's focused at a different distance.
E) you will see your image at your same height.

Question 23

A negative magnification for a mirror means

A) the image is inverted, and the mirror may be concave or convex.
B) the image is upright, and the mirror is convex.
C) the image is inverted, and the mirror is convex.
D) the image is inverted, and the mirror is concave.
E) the image is upright, and the mirror may be concave or convex.

Question 24

The image of the rare stamp you see through a magnifying glass is

A) always upside-down compared to the stamp.
B) either the same orientation or upside-down, depending on how close the stamp is to the glass.
C) either the same orientation or upside-down, depending on the thickness of the glass used.
D) always the same orientation as the stamp.

Question 25

If you stand in front of a double-concave mirror, exactly at its center of curvature, your image will appear where you are, but

A) larger and upside down.
B) the same size and upright.
C) larger and upright.
D) the same size and upside down.

Question 26

The images formed by concave lenses

A) could be real or virtual; it depends on whether the object distance is smaller or greater than the focal length.
B) are always virtual.
C) could be real or virtual, but always real when the object is placed at the focal point.
D) are always real.

Question 27

Compare two diverging lenses similar except that lens B is rated at 20 Diopters, whereas lens A is rated at 10 Diopters. The focal length of lens B is

A) twice the focal length of lens A.
B) 1/ of the focal length of lens A.
C) one-half of the focal length of lens A.
D) one-fourth of the focal length of lens A.
E) four times the focal length of lens A.

Question 28

What kind of lens is it that has a power of +10 Diopters and a first surface center of curvature in front of the lens?

A) double convex
B) converging meniscus
C) plano concave
D) double concave
E) plano convex

Question 29

Which of the following aberrations does not apply to mirrors?

A) astigmatism
B) spherical
C) coma
D) chromatic

Question 30

Spherical lenses suffer from

A) both spherical and chromatic aberration.
B) chromatic aberration, but not spherical aberration.
C) neither spherical nor chromatic aberration.
D) spherical aberration, but not chromatic aberration.

Question 31

If the refractive index of the glass in a lens varies with wavelength, then which of the following results?

A) astigmatism
B) chromatic aberration
C) light scattering
D) total reflection
E) spherical aberration

Question 32

Spherical aberration can occur in

A) mirrors but not lenses.
B) lenses but not mirrors.
C) mirrors and lenses.

Question 33

Chromatic aberration occurs because of

A) spherical surfaces.
B) astigmatism.
C) internal reflection.
D) dispersion.
E) polarization.

Question 34

See Figure 23-4. When two parallel white rays pass through the outer edges of a converging glass lens, chromatic aberration will cause colors to appear on the screen in what order, from the top down?

A) blue, blue, red, red
B) red, blue, red, blue
C) blue, red, blue, red
D) blue, red, red, blue
E) red, blue, blue, red

Question 35

A man 190. cm tall stands 25. m from a plane wall mirror. One meter in front of him sits his dog, 30. cm tall. What minimum mirror size is needed for the man to see all of his dog's reflection?

Question 36

At an amusement park you stand between two plane mirrors, which intersect at an angle of 60°. You are positioned at point P in Figure 23-5. You are 1.0 m from the nearest mirror, and 15° above it.

What is the distance from you to the nearest image and to the second nearest image?

Question 37

Describe a mirror which takes an object at a distance of 47. cm and forms a real image at 23. cm.

Question 38

An object is placed 3 cm from a convex mirror of radius 4 cm.
(a) Graphically determine the size and position of the image.
(b) Is the image real or virtual?

Question 39

An object is placed 6 cm from a concave mirror of radius 4 cm. Graphically determine:
(a) the image position.
(b) if the image is larger, smaller, or the same size as the object.
(c) if the image is real or virtual.

Question 40

A slide projector has a lens of focal length 150. mm. An image 100. cm × 100. cm is formed of a slide whose dimensions are 50.0 mm × 50.0 mm. How far from the lens must the screen be placed?

Question 41

Where must an object be placed with respect to a converging lens of focal length 30 cm if the image is to be virtual, and three times as large as the object?

Question 42

A lens projects an image of a man as seen in Figure 23-8. Rays marked A, B, and C travel to the lens from the man's ear.


Draw the three refracted rays as they proceed to the right of the lens; noting that A is parallel to the axis, B goes through the center of the lens, C proceeds to the bottom of the lens, and the point marked f is the focal point of the lens.

Question 43

An object is placed at the origin. A converging lens of focal length 10 mm is placed at x = 40 mm on the x axis. A second converging lens of focal length 20 mm is placed at x = 90 mm. Graphically determine the size and location of the final image.

Question 44

What POWER lens placed next to a lens of 25. cm focal length would produce a combination with an effective INFINITE focal length?

Question 45

A converging lens with the same curvature on both sides and focal length 25. cm is to be made from crown glass (n = 1.52). What radius of curvature is required for each face?

Question 46

A camera uses a biconvex lens made of glass with an index of refraction of 1.60 and has a radius of curvature of 12. cm for the 1st surface and 24. cm for the 2nd.
(a) What is the focal length of this lens when used in air?
(b) If used under water (n = 1.33), what is the focal length?

Question 47

A double convex lens has faces of radii 18.0 cm and 20.0 cm. When an object is placed 24.0 cm from the lens, a real image is formed 32.0 cm from the lens. Determine:
(a) the focal length of the lens.
(b) the index of refraction of the lens material.

Question 48

A 4.0 cm high object is 20. cm in front of a 1.333 Diopter plano-convex lens.
(a) Find the image position. Real or Virtual?
(b) Find the image size. Erect or Inverted?

Question 49

An object is located 2.6 m in front of a plane mirror. The image formed by the mirror appears to be

A) on the mirror's surface.
B) 2.6 m behind the mirror's surface.
C) 1.3 m in front of the mirror.
D) 2.6 m in front of the mirror.
E) 1.3 m behind the mirror's surface.

Question 50

A person approaches a plane mirror at a speed of 2 m/s. How fast does he approach his image?

A) 3 m/s
B) 1 m/s.
C) 1 m/s
D) 4 m/s
E) 2 m/s

Question 51

If you place a plane mirror vertically into water, and a dolphin moves toward it with a speed of 4 m/s, she will see her image move toward her at a relative speed of

A) 6. m/s.
B) 2. m/s.
C) 4. m/s.
D) 10. m/s.
E) 8. m/s.

Question 52

A object is 20 cm in front of a concave mirror, and the image is 5.0 cm in front of the mirror. What is the focal length of the mirror?

A) 25 cm
B) 0.25 cm
C) 2.1 cm
D) 6.7 cm
E) 4.0 cm

Question 53

When an object is placed 60. cm from a converging lens, it forms a real image. When the object is moved to 40. cm from the lens, the image moves 10. cm farther from the lens. What is the focal length of the lens?

A) 20. cm
B) 40. cm
C) 30. cm
D) 50. cm
E) 42. cm

Question 54

How far from a lens of focal length 50.0 mm must the object be placed if it is to form a virtual image magnified in size by a factor of three?

A) 38.3 mm
B) 54.4 mm
C) 33.3 mm
D) 48.0 mm
E) 42.2 mm

Question 55

A 4.0 cm tall object is placed 50 cm away from a converging lens of focal length 25 cm. What is the nature and location of the image?

A) The image is real, 2.5 cm tall, 25 cm on the same side as object.
B) The image is real, 4.0 cm tall, 50 cm on the other side of the lens.
C) The image is virtual, 4.0 cm tall, 50 cm on the same side as object.
D) The image is virtual, 2.0 cm tall, 15 cm on the other side of the lens.
E) The image is virtual, 2.5 cm tall, 25 cm on the other side of the lens.

Question 56

Two very thin lenses, each with focal length 20. cm, are placed in contact. What is the focal length of this compound lens?

A) 40. cm
B) 30. cm
C) 15. cm
D) 10. cm
E) 20. cm

Question 57

Light from an object proceeds through 3 lenses, each with magnification 2, -4, 0.2 respectively. The overall magnification is

A) +8/5.
B) 2 x (-4) × 0.2 = -1.6.
C) +5/8.
D) 2 - 4 + 0.2 = -1.8.
E) 2/(-4)/0.2 = -2.5.

Question 58

A plano-convex lens is to have a focal length of 40 cm. It is made of glass of index of refraction 1.65. What radius of curvature is required?

A) 32. cm
B) 44. cm
C) 26. cm
D) 13. cm
E) 36. cm

Question 59

A double convex (convex-convex) thin lens has radii of curvature 46. cm, and is made of glass of index of refraction n = 1.60. What is the focal length?

A) 36. cm
B) infinite
C) 18. cm
D) 38 cm
E) 46. cm

Question 60

What Diopter takes an object at 47. cm and forms an upright image 23. cm from the lens?

A) -0.022 D
B) -2.2 D
C) 2.2 × 10² D
D) +0.022 D
E) +2.2 D

Question 61

A concave meniscus lens with an index of refraction of 1.48 has radii of 6.0 cm and 4.0 cm (see Figure 23-11)

What is the power of the lens in DIOPTERS?

A) -0.25
B) -0.040
C) -20.
D) -0.20
E) -4.0