exam_2_review

# Exam 2 review

The following questions and problems are courtesy of Justin Dunlap

## Practice Questions, May 13 Lecture

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

### Review question 1

The focal lengths of the objective and the eyepiece in a microscope are 0.29 cm and 2.5 cm, respectively. An object is placed 0.3 cm from the objective. The image of this object is viewed with the eyepiece adjusted for minimum eyestrain. What is the distance between the objective and the eyepiece?

• [ X ] A) 11.2 cm
• [….] B) 10.1 cm
• [….] C) 10.4 cm
• [….] D) 11.5 cm
• [….] E) 9.85 cm

### Review question 2

A magnifying glass uses a converging lens with a refractive power of 20 diopters. What is the magnification if the image is to be viewed by a relaxed eye with a near point of 25 cm?

• [ X ] A) 5.0
• [….] B) 4.0
• [….] C) 1.0
• [….] D) 3.0
• [….] E) 2.0

### Review question 3

What is the power of a lens that has a focal length of $-40$ cm?

• [….] A) $-4.0$ diopters
• [….] B) $+4.0$ diopters
• [….] C) $+2.5$ diopters
• [….] D) $+2.7$ diopters
• [ X ] E) $-2.5$ diopters

### Review question 4

To burn a hole in a piece of paper using light from the Sun, which mirror would work the best?

• [….] A) Convex.
• [….] B) Plane.
• [ X ] C) Concave.
• [….] D) All of the given answers would work equally as well.
• [….] E) None of the given answers would burn a hole.

### Review question 5

You have a choice between two lenses of focal lengths $f_a$ and $f_b = 2 f_a$ to use as objective lens in building a compound microscope. If the magnification you obtain using lens a is $M_a$, what will be the magnification when using lens b?

• [….] A) $M_b = \frac{1}{4} M_a$
• [ X ] B) $M_b = \frac{1}{2} M_a$
• [….] C) $M_b = 8 M_a$
• [….] D) $M_b = 4 M_a$
• [….] E) $M_b = 2 M_a$

### Review question 6

Which of the following expressions is correct for the transmitted intensity of an unpolarized beam of light with an intensity $I_i$ passing through a polarizer?

• [….] A) $I_t = 2 I_i$
• [ X ] B) $I_t = \frac{1}{2} I_i$
• [….] C) $I_t = I_i$
• [….] D) $I_t = 4 I_i$
• [….] E) $I_t = \frac{1}{4} I_i$

### Review question 7

Spherical mirrors suffer from

• [….] A) neither spherical nor chromatic aberration.
• [….] B) chromatic aberration, but not spherical aberration.
• [ X ] C) spherical aberration, but not chromatic aberration.
• [….] D) both spherical and chromatic aberration.

### Review question 8

A nearsighted person has a far point that is 4.2 m from his eyes. What focal length lenses must he use in his contact lenses to allow him to focus on distant objects?

• [….] A) $-5.2$ m
• [….] B) $4.8$ m
• [….] C) $4.2$ m
• [ X ] D) $-4.2$ m
• [….] E) $5.2$ m

### Review question 9

Jill is farsighted and cannot see objects clearly that are closer to the eye than 80.0 cm. What is the focal length of the contact lenses that will enable her to see objects at a distance of 25.0 cm from her eyes?

• [….] A) $+32.5$ cm
• [….] B) $-36.4$ cm
• [….] C) $-21.2$ cm
• [ X ] D) $+36.4$ cm
• [….] E) $+21.2$ cm

### Review question 10

An object is placed in front of a convex mirror at a distance larger than twice the focal length of the mirror. The image will appear

• [….] A) upright and enlarged.
• [ X ] B) upright and reduced.
• [….] C) inverted and enlarged.
• [….] D) inverted and reduced.
• [….] E) in front of the mirror.

### Review question 11

Which one of the following is the correct number for the magnification of a plane mirror?

• [….] A) 2.0
• [….] B) 1.5
• [ X ] C) 1.0
• [….] D) 0.25
• [….] E) 0.5

### Review question 12

A vertically polarized beam of light of intensity $100\frac{\text W}{\,{\text m}^2}$ passes through a polarizer with its transmission axis at 40.0$^\circ$ to the vertical. What is the transmitted intensity of this beam of light?

• [ X ] A) $58.7\frac{\text W}{\,{\text m}^2}$
• [….] B) $0\frac{\text W}{\,{\text m}^2}$
• [….] C) $100\frac{\text W}{\,{\text m}^2}$
• [….] D) $44.4\frac{\text W}{\,{\text m}^2}$
• [….] E) $25.0\frac{\text W}{\,{\text m}^2}$

### Review question 13

The length of a telescope is 2.00 m and the focal length of the objective is 2.0 cm. What is the focal length of the eyepiece?

• [….] A) 200 cm
• [….] B) 101 cm
• [ X ] C) 198 cm
• [….] D) 202 cm
• [….] E) 2.0 cm

### Review question 14

John's face is 20 cm in front of a concave shaving mirror of focal length 30 cm. How large an image does he observe?

• [….] A) of the same size as his face
• [….] B) twice as large as his face
• [….] C) half as large as his face
• [….] D) four times as large as his face
• [ X ] E) three times as large as his face

### Review question 15

A simple refracting telescope provides large magnification by employing

• [….] A) a long focal length objective and a long focal length eyepiece.
• [….] B) a short focal length objective and a long focal length eyepiece.
• [….] C) a short focal length objective and a short focal length eyepiece.
• [ X ] D) a long focal length objective and a short focal length eyepiece.

## Practice Problems, May 13 Lecture

Solve three of the four problems (cross out the one you do not want graded). Show all of your work to receive full credit, most importantly show all the formulas you used to find the final answers. No credit will be awarded if an answer is given without work shown.

### Review problem 1 The lens system above has focal lengths $f_1 = 45.0$ cm, $f_2 = -50.0$ cm, object height $h_o = 40.0$ cm, the distance of the object from the first lens $d_o = 70.0$ cm, and the distance between the two lenses equal to $L=200$ cm:

• a) Using at least two light rays, on the drawing above sketch the location and size of the image after passing through the first lens as well as the location and size of the final image. (You may change which two rays you use for each lens.) (4 pts)
• b) How far away is the final image from the object? (6 pts)
• c) What is the total magnification of the two lens system? (3 pts)
• d) What is the height of the final image? (2 pts)

### Review problem 2

A meter stick lies along the principal axis of a convex mirror with a focal length of 30.0 cm. Two 10.0 cm toy figures are placed upright on near and far end of the meter stick. The closer of the two figures is 50.0 cm away from the mirror. • a) How far away from the mirror is the image of the figure that is closest to the mirror? (4 pts)
• b) How far away from the mirror is the image of the figure that is furthest from the mirror? (4 pts)
• c) What is the length of the image of the meter stick? (in other words, what is the distance between the two images of the figures?) (1 pts)
• d) How tall is the closer of the two figures to the mirror in the image? (2 pts) Is it upright or inverted? (1 pt)
• e) How tall is the farther of the two figures from the mirror in the image? (2 pts) Is it upright or inverted? (1 pt)

### Review problem 3

Match the definitions and descriptions with the best term or phrase given below (1.5 pts each):

 polarizer’s transmission axis polarization rays wave fronts specular reflection diffuse reflection focal point index of refraction total internal reflection Snell's law sign conventions incident angle angle of reflection angle of refraction focal length magnification image distance object distance real object virtual object real image virtual image concave mirror convex mirror converging lens diverging lens Brewster's angle critical angle nearsighted farsighted refractive power diopter far point near point magnifying lens telescope compound microscope aberration spherical aberration chromatic aberration dispersion rainbow
1. A lens with a negative focal length.
• diverging lens
2. A problem in lenses where different colors of light are focused to different focal points.
• chromatic aberration
3. The angle of incidence of light such that after striking a surface the reflected light is completely polarized.
• Brewster's angle
4. Reflection from a rough surface such that light is sent out in a variety of directions.
• diffuse reflection
5. Light rays converge towards this type of object. The sign convention for the distance to the object in this case is negative.
• virtual object
6. The ability of a lens to refract light (commonly measured in diopters)
• refractive power
7. A problem in lenses and mirrors of a particular shape where light further away from the principal axis is focused to a different point than light closer to the principal axis.
• spherical aberration
8. The length of this device is the sum of the two focal lengths of the lenses used to make it
• telescope
9. A property of a material that is related to how fast light travels in the material
• index of refraction
10. Colorful object seen in the sky due to the dispersion of light in raindrops.
• rainbow

### Review problem 4

While wandering on Mars (which has little atmosphere and can be considered a vacuum environment), you stumble upon a mysterious cube of an unknown material. You have a red and a blue laser handy and perform a few experiments. You observe that total internal reflection occurs at the critical angle of 19.5$^\circ$ for red light.

1. To observe total internal reflection did you scrutinize a ray of light going from the mystery material to vacuum or a ray of light going from vacuum to the mystery material? ( 1 pt)
2. What is the index of refraction of the material for red light? (4 pts)
3. What is the speed of red light in the material? (3 pts)
4. What is Brewster's angle for red light going from vacuum to the mystery material? (3 pts)
5. Would the critical angle for blue light be greater or smaller than that of red light? (1 pt). Why? (3 pts) (Hint: You can safely make the assumption that this mystery material behaves like glass for the frequency dependence of the index of refraction.) 