Physics 1230 Light and Color Fall 2007 M. Goldman Tues., Oct. 4, 2007

Solution to Exam #1 White version 1

This exam will be worth 100 points. There are 10 multiple choice questions worth 4 points each and 3 problems worth a total of 60 pts. Please put your answers to the multiple choice probems on a properly filled out bubble sheet. There will be no partial credit for the multiple choice problems. Your answers to the problems should be on this exam (not the bubble sheet) in the space provided.

Your full name:
Last ______________________________________________________________
First and middle ____________________________________________________

Equations

Lens eqn: 1/f = 1/x_o + 1/x_i

f = focal length of lens (positive for convex converging lens)

x_o = distance from center of lens to object

x_i = distance from center of lens to image (positive if on opposite side of lens from object)

Magnification eqn: M = s_i/s_o = -x_i/x_o

s_i = size of image (perpendicular to axis)

s₀ = size of object (perpendicular to axis)

Relationship between frequency and wavelength of light: l·n = c

l = wavelength

n = frequency

c = speed of light (3 x 10⁸ m/s in empty space)

Bending power of a lens: P = 1/f

P = power in diopters

f = focal length of lens in meters

Combined power of two thin lenses in contact: P₁ + P₂ = P

P₁ = power of lens 1; P₂ = power of lens 2; P = power of combined lenses

Part 1 (40 pts)

Ten multiple choice questions, 4 points each

1) The image of your nose in a plane mirror is

a) at a distance in back of the mirror equal to the distance of your nose in front of the mirror

b) created after rays from your nose are specularly reflected from the mirror and seen when the reflected rays enter your eyes

c) Both of the above

d) None of the above

2) You are looking towards the sun while standing on Earth in the penumbra of the moon. At that moment you are seeing

a) A total eclipse of the sun

b) A partial eclipse of the sun

c) A total eclipse of the moon

d) A partial eclipse of the moon

e) None of the above

3) Two thin magnifying glasses each have the same focal length of 10 cm. What is the effective focal length of the combined lenses when they are touching each other?

a) 5 cm, b) 10 cm, c) 20 cm, d) 10 m, e) 1 cm

4) Can a concave shaving mirror aimed at the sun be used to burn a hole through a piece of tissue?

a) No, because the image is virtual.

b) No, because the sun is too far away away from the center of the concave mirror.

c) Yes, if the tissue is put at the center of the concave mirror.

d) No, because the sun is not located at the focal point.

e) Yes, if the tissue is put at the focal point of the concave mirror.

5) White sunlight incident on a raindrop comes out as a rainbow because

a) The rays from the sun slow down progressively as they advance in the raindrop.

b) The rays from the sun reflect from the back of the raindrop

c) The speed of light in a raindrop is slightly different for each of the wavelengths of light.

d) The raindrop has resonances at the various frequencies corresponding to the various colors of the rainbow.

e) The raindrop is colored,

6) A virtual image

a) Can be seen from any and all angles

b) Has rays of light from the object actually crossing at its location after being reflected or refracted

c) Is always the same size or larger than a real image

d) Will not appear if a screen is placed at its location

e) Is said to be virtual because it cannot be seen

7) A mirage occurs when cold air gradually heats up in air layers closer to the ground. Where is the speed of light slowest?

a) Close to the ground b) Higher up c) It is always the same.

8) White light with a higher color temperature compared to white light with a lower color temperature appears

a) Redder b) Bluer c) The same

9) As the frequency of an electromagnetic wave in empty space gets larger

a) The amplitude of the wave gets smaller

b) The amplitude of the wave gets larger

c) The speed of the wave gets slower

d) The wavelength of the wave gets larger

e) The wavelength of the wave gets smaller

10) A pinhole camera makes an image of an object by

a) Focusing most rays from each object point

b) Refracting most rays from each object point

c) Reflecting most rays from each object point

d) Blocking most rays from each object point

e) Dispersing most rays from each object point

Part II (60 pts): Problem solving (answer all parts and show your work)

11) [20 pts]

a) Does the woman see the man standing in the water up to his chest as shorter, taller or the same height as he really is. Explain using words and ray tracing from the x on the man's fin to her eye. (10 pts)

b) What does the child snorkeler with eyes very near the surface of the water see when he looks up in the direction shown? Explain using words and ray tracing (10 pts)

boy looks in

this direction

a) The red ray coming from the x on the man's fin bends away from the normal as it exits into air and goes into the woman's eye. She thinks she sees the x along the straight line backward extension of the ray that enters her eye. She therefore sees it as above where it really is. This is the same for all of the rays coming from the man's body below the water line so that he seems shorter, as in the photograph at left.

b) The boy sees the totally internally reflected (blue) rays from the top of the man's shorts while he is in the water. However, the boy thinks it is coming from the backward extension of the ray entering his eye. The boy therefore sees an upside down image of the top of the man's shorts which appears to be above the water.

12) [20 pts] Alex's image is 4 cm from a lens while he is 12 cm from the lens. on the same side as his image. Use the appropriate formulas and show all work in answering the following questions:

a) What is the focal length of the lens and is it a convex or a concave lens? (9 pts)

Given: x₀ = 12 cm, x_i = -4 cm (minus sign because image is on the same side of the lens as the object)

Find: Focal length, f

1/f = 1/x_o + 1/x_i = 1/12 - 1/4 = 1/6, so f = -6 cm. This is negative, so the lens is concave (diverging)

b) What is the magnification? Is his image larger or smaller than Alex? (4 pts)

M = -x_i/x₀ = -(-4/12) = 1/3. His image is smaller. It is 1/3 as large as Alex

c) Is it real or virtual? Upside down or rightside up? (4 pts)

Since x_i is negative the image is virtual. Since M is positive it is right side up.

d) Can Alex see his own image from where he is? Why? (3 pts)

No, he can't see his image. He could only see his image if he were on the other side, since no rays from the image reach his eyes. (See similar example below using ray-tracing).

13) [20 pts] The gleam in the eye of the rat, Remy, in the movie Ratatouille may be thought of as the image of a light bulb as seen in a convex (outward-bulging) reflecting spherical surface.

Use rays of type 1, 2 and/or 3 to find the location of the image of the light bulb shown below relative to the surface of Remy's eyeball. Sketch the image of the light bulb. Is it real or virtual? Smaller or larger? Right side up or upside down?

Where is this round white image of the light bulb when the eyeball is viewed from the side?