Homework Part I: Optics 50 points

Chapter 22-23

1. List all of the major formulas (equations) and define the variables

-be sure to define what the different q’s mean. (for example, are they the angle between the mirror and the light ray or are they the angle between a normal line to the mirror and the light ray…etc)

2. Copy the following figures/tables onto that paper. These are all of the possible permutations for curved mirrors and lenses. It also includes when you would use + and – conventions for the values in the equations.

a. fig 23.1 p. 711

b. fig 23.2 p. 712

c. fig 23.5 p. 715

d. fig 23.7 p. 717

e. fig 23.8 p. 718

f. fig 23.15 p. 726

g. fig 23.18 p. 731

h. Table 23.1 p. 712

i. Table 23.2 p. 721

j. Table 23.3 p. 727

22.1 Wave fronts and rays

2

22.2 Reflection

10, 12

12: Start by drawing it. Use your geometry knowledge (rusty as it may be) and do things like subtracting from 90^o and 180^o when necessary. Don’t forget that q_i = q_r

22.3-22.4 Refraction and Total internal reflection and fiber optics

18, 19, 20, 21, 22, 26, 28, 35, 52, 55, 65

28: n₁sinq₁ = n₂sinq₂

52: d’=d/n

55: a) n₁sinq₁=n₂sinq₂ where q₁= 45^o. b) q_c = sin^-1sin (n₂/n₁)

Chapter 23

23.1 Plane Mirrors

1, 2, 6, 8, 14

14: Mirrors must be 1/2 as tall as an object. Remember that 10 cm = 0.01 m. Realize that it is not possible to back up further and see more of yourself in a mirror. This is a common misconception.

23.2 Spherical Mirrors

17, 18, 19, 20, 22, 23, 27, 28, 29, 43, 44

27: do is + and di is –

28: see fig 23.8 p. 718. First use d_i= d_of/d_o-f. Then, use the value you find for d_i to put it into the equation for magnification (M = -d_i/d_o). Then, remember that M=-d_i/d_o and M= h_i/h_o so you can solve for h_i using the value for M you find and the value for h_o given in the problem. Be sure you use the correct sign convention when solving these. Consult tables 23.2 and 23.3 if you don’t know which signs to use.

43: f = R/2 and d_i = -Md_o. Realize that M = +/- 2 since twice the height would mean twice the magnification (either bigger, +, or smaller, -).

44: Convert all lengths into meters (or centimeters – but use only ONE unit)

23.3 and 23.4 Lenses and Lens Aberrations

46, 47, 48, 49, 54, 55, 57, 61, 63, 64, 66, 68

49: Think of the bowl as a spherical lens and where would the focal point be in relation to the fish? What image would this cast? Where would it be? Would it be real or virtual? Would it be inverted? Think about your experiences with fishbowl gazing.

54/55: Look at hint for question #28 above. You can use the same formulas. Be sure to draw the ray diagrams.

61: d_i= d_of/d_o-f. and d = d_o+d_i = d_o+(d_of/d_o-f ) = [d_o(d_o-f)/d_o-f]+[d_of/d_o-f]= d_o²/d_o-f

Notice that the quantity: d_o²/d_o-f reaches its minimum when d_o = 2f. So, the minimum distance would be 4f

63: we know from #61 that 4f is the minimum distance (between object and image) for a sharp image to form. At this distance, d_o=d_i=2f so M = -d_i/d_o = -1 (a real image). Therefore, the minimum distance for a real image is also 4f.

b) for a biconvex lens, virtual image forms when 0 < d_o < f. When d_o approaches,

d_i = d_of/d_o-f also approaches 0. So, the distance between the object and the image approaches 0.

66: First solve d_i for the lens. Also solve the Magnification for the lens.

Next, solve for the d_i mirror and M_mirror.

68. First solve d_i for the objective lens.

Next, solve for the d_i eyepiece

Answers:

Chapter 22:

2. c

10: 55^o

12: 20^o

18: b

20: yes, no, yes

22: n1>n2 and q1>qc

26: 1.45

28: 41o

52: 1.6 cm

Chapter 23:

2: c

6: +1

8: a) 4.0 m b) upright, virtual, same size

14: a) 0.855 m b) 0.855 m

18: a

20: concave side of spoon gives inverted image. Convex side is upright.

b) if you are very close (inside of the center of curvature) you can see an upright image.

22: The image of a distant object (at infinity) is formed on a screen in the focal plane. The distance from the vertex of the mirror to the plane is the focal length.

28: a) 24 cm, 1.8 cm real and inverted

b) 30 cm, 3.0 cm, real and inverted

c) infinity so the image is not defined

d) -7.5 cm, 4.5 cm, virtual and upright

44: a) d_i = -39.8cm, h_i = 0.80 cm b) d_i = -38.5 cm, h_i = 7.7 cm

46: d

48: b

54: a) -47 cm, M = +3.14 h_i = 13 cm virtual and upright

b) 57 cm, M = -1.57, h_i = 6.3 cm real and inverted

64: 4.2 cm

66: 0.26 m in front of the concave mirror; M_total = 0.60, real and upright

68: 18 cm to the left of the eyepiece; virtual image.