spring 2015 physics 123 exam 2 solution

Name ___________________________________Student ID ____________ Score_______ last first

Physics 123, Spring 15 Exam 2, page 1

Mirror surface

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+

++

I. Lab questions With your head at tabletop height, and with one eye open, you see Figure 1. You close your eye, and after your head is moved to the left you open your eye and you see Figure 2. You notice that the angular width of all three objects is the same. 1. (4 pts) Rank the actual width (w) of the pieces from widest to narrowest.

A. wA = wC > wB B. wA > wB > wC C. wA = wB = wC D. wC > wB > wA E. Impossible to tell from the information given.

2. (4 pts) You are looking at the mirror depicted in

the figure at right. Which images, if any, can you see?

A. Just the star. B. Just the hexagon. C. The circle and the hexagon. D. The star and the hexagon. E. None of them, the mirror is too short.

3. (4 pts) You are looking at the mirror depicted in the figure below. Which images, if any, can you see?

A. Just the star. B. Just the hexagon. C. The circle and the hexagon. D. The star and the hexagon. E. None of them, the mirror is too short.

L CA

B

Figure 1 Figure 2

Mirror surface

Barrier

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II. Light and Polarization. An unpolarized plane wave (light) of frequency 5.661014 Hz and intensity 25.0 W/m2, passes through three ideal polarizers. The first has a horizontal transmission axis, and the other transmission axes are each rotated by with respect to the previous one, as shown.

4. (3 pts) Which choice best represents the color of the incoming light?

A. Blue-violet B. Green C. Yellow-Orange D. Red E. None of these 5. (3 pts) Which choice best describes the outgoing light, after passing all polarizers?

A. Right Circularly Polarized Light (RCP). B. Left Circularly Polarized Light (LCP). C. Linearly polarized light with E at 2 to the horizontal. D. Linearly polarized light with E at (/2 - 2) to the horizontal. E. Mixture of polarized light, half with E at and half with E at 2 to the horizontal.

6. (4 pts) Which choice best represents the intensity of the outgoing light if the angle = 30?

14 W/m2 9.7 W/m2 9.4 W/m2 7.9 W/m2 7.0 W/m2 A B C D E

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2 out



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III. Reflection & Refraction. A light ray in air strikes a glass surface (n = 1.60) at 35.0 to the surface as shown.

7. (4 pts) Which choice best represents the angle G for the light ray in the glass? 21 31 39 53 59

A B C D E 8. (4 pts) Now a light ray in the glass (n = 1.60) strikes the same surface at 35.0 to the surface

as shown. Which choice best describes the light that emerges into the air?

A. Light emerges at a large angle to the surface, A > 35. B. Light emerges at a small angle to the surface, A < 35. C. Light emerges at the same angle to the surface, A = 35. D. No light is able to emerge: total internal reflection.

IV. Light & Images 9. (3 pts) Converging lenses can produce either real or virtual images, depending on the

placement of the object and observer. If you use a single converging lens to view a virtual image, and also a real image, in what way(s) will the images be observed to differ?

A. Real image is inverted compared to the object, virtual image is erect. B. Real image looks more real than the virtual image (which appears fake). C. Real image is more sharply focused than the virtual image. D. More than one of these is true. E. None of these is true.

Lenses constructed of a single material often cause chromatic aberration, a condition where light of different colors is refracted at slightly different angles by the lens. The index of refraction for a certain lens varies linearly with the wavelength of light over the range between

660 nm 480 nm1.676 and 1.728n n . 10. (2 pts) Which color of light will be refracted more noticeably by this lens? A. Red B. Yellow C. Green D. Blue E. All the same 11. (4 pts) A converging lens is made of this material with radius of curvature on each side of

magnitude 19.0 cm. Which choice best represents the focal length of this lens for light of wavelength 480 nm?

A. 13 cm B. 14 cm C. 26 cm D. 28 cm E. None of these

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V. Ray Optics and Images A converging lens with focal length f1 = +12.5 cm is placed 25.0 cm from a converging mirror of focal length f2 = +10.0 cm as shown. The top of the lens is flattened to allow a bright, 2.5-cm-tall object to be attached to the top of the lens, as shown. Lens focal points are dots, mirror focal point is . An observer is located on the far left.

15. (8 pts) Using the mirror-lens equation, compute the location of each image produced by the

lens-mirror system. Show your work. Light from object does not pass through lens first, so encounters the mirror first

11

1 1 1 1 1 1 for mirror 16.7 cm25.0 10.0

ii o f i

Using this image as the object for the lens, it is 25-16.67 = 8.33 cm from the lens, so:

22

1 1 1for lens 25.0 cm8.33 12.5

ii

This is the final image, and it is located at the same horizontal position as the mirror. It is worth noting that the bottom of each image does NOT extend all the way down to the axis of symmetry of the lens-mirror system. For ray diagram, first image uses orange-red rays, second uses blue-green. 16. (12 pts) Draw, directly on the figure above, a ray diagram to locate all images produced as

light passes through the lens-mirror system. Include at least two rays (with arrowheads to show direction of travel) to locate each image, and show rays traced backward to locate virtual images, if necessary, as dashed lines. Use a ruler to insure straight lines.

17. (5 pts) What is the magnification achieved with this combination? Justify your answer.

Linear magnification: 1 21 21 2

16.7 25* 2.0025 8.33

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Angular magnification is inappropriate for this case. Ray diagram is consistent with this ONLY if images do not extend down to the axis.

Object on lens

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Name ______________________________________ Student ID _______________ Score________ last first

Physics 123A&B, Spring 2015 Exam 2 WO-UWA123AC152T-E2(EMW)Sol.doc

VII. [20 points total] This problem consists of two unrelated parts, A and B. A. An electromagnetic plane wave travels through empty space. At the instant shown (t = 0), the electric

field at z = 0 points in the +y direction and the magnetic field at z = 0 points in the +x direction. i. [5 pts] At point A which direction does the

magnetic field vector point, one-eighth (1/8) of a period after the instant shown at right? Explain. From the Poynting vector it can be determined that the wave is propagating in the negative z direction, therefore one-eighth of a period later the magnetic field should still point in the negative x direction.

ii. [5 pts] Write possible equations for both the electric and magnetic fields that could represent this EM plane wave for all space and time. Express your answer in terms of Eo, Bo, k, and . Assume Eo, Bo, k, and are all positive values.

E (x, y,z,t) = Eo cos(kz +t) y and

B (x, y,z,t) = Bo cos(kz +t) x . Using a phase shift, we could also write

E (x, y,z,t) = Eo sin(kz +t + 2) y and

B (x, y,z,t) = Bo sin(kz +t + 2) x

B. The mathematical representation of a different electromagnetic plane wave is shown below together with a pictorial representation of the wave at some arbitrary time t1. Several devices (each consisting of a bulb and very thin, straight-wire segments, identical to the one at right) are held at locations 1, 2, 3, and 4 as indicated below. All devices lie in the x-y plane. Bulb 2 is located at an angle with respect to the y-axis. Assume Eo, Bo, k, and are all positive values.

E

x

y

B z

1

3

4

2

At some arbitrary time t1

i. [5 pts] Rank the four bulbs according to their average brightness from brightest to dimmest using

> and/or = signs. If any of the bulbs do not light, state so explicitly. Explain. For a bulb to light, its wire must have a component parallel to E, as the electric force F = qE is what accelerates the charges in the wire. Bulbs 2, 3, and 4 will all light. The wire of bulb 2, however, is not parallel with E, so it will be dimmer than bulbs 3 and 4. Bulb 1s wire is perpendicular to the electric field so it will not light. The ranking is as follows: Bulb 3 = Bulb 4 > Bulb 2 > Bulb 1 = 0

ii. [5 pts] At x = 0 and t = 0, in which direction does the magnetic field vector point? If the magnitude of the magnetic field at that location and time is zero, state so explicitly. Explain. Using the mathematical representation of B given above, we find

B = Bo sin( 2) z . Therefore the equation will give the maximum positive value of B. Thus the direction of the magnetic field at x=0 and t=0 is the +z direction.

E

B

x

y

z

A

At time t = 0

Wire

Bulb

B (x, t) = Bo sin(kx t + 2) z

E (x, t) = Eo sin(kx t + 2) y

spring 2015 physics 123 exam 2 solution

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