### Spring 2004 Physics 102 Hour Exam 3(27 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

This exam consists of 27 questions; true-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 105. The exam period was 90 minutes; the mean was 88.4; the median was 91. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

This and the next three questions are about the following situation:

A concave spherical mirror of focal length 10 cm is used to observe distant objects.

At what distance from the mirror will the distant objects be focused?

(a)   5 cm
(b)   10 cm
(c)   20 cm

### QUESTION 2*

The image is

(a)   upright, magnified.
(b)   upright, reduced.
(c)   inverted, magnified.
(d)   inverted, reduced.
(e)   upright, neither magnified nor reduced.

### QUESTION 3**

Would the image be larger and/or brighter if the size of the mirror were increased, while keeping the focal length at 10 cm?

(a)   The image would be larger and brighter.
(b)   The image would only be brighter.
(c)   The image would not change.

### QUESTION 4**

If the focal length were changed to 1 m, what would happen to the image?

(a)   It would increase in size.
(b)   It would decrease in size.

### QUESTION 5*

A swimmer underneath the water (n = 1.33) looks up to the surface of the water and sees the sun as it goes below the horizon of the lake. What is the approximate angle Φ that the sun appears to be above the horizon from the point of view of the swimmer?

(a)   35.3°
(b)   41.2°
(c)   45.6°
(d)   50.8°
(e)   55.7°

### QUESTION 6***

You have the idea of building a flat mirror using total internal reflection instead of a reflecting metal surface. You choose to use a single layer of glass with index of refraction 1.4 as your material. If the glass is 1 cm thick, over what range of viewing angles (from the normal) would the glass work as a perfectly reflecting mirror?

(a)   0° - 90°
(b)   45.6° - 90°
(c)   None of the above.

### QUESTION 7***

If you used two layers of material, one on the top with n1 = 1.2 and the other on the bottom with n2 = 1.4, what would your answer be?

(a)   45.6° - 90°
(b)   56.4° - 90°
(c)   None of the above.

### QUESTION 8**

You wish to look at the cat which is standing around a corner but you want to stay where you are, clear of the cat's claws. Which of the arrangements 1, 2 or 3 of plane mirrors (shown immediately below), placed in the shaded square in figure A below, would allow you to see the cat in the orientation shown in figure B? The direction in which you are looking is shown as an arrow. Please note that both sides of each mirror are reflecting surfaces.

(a)   1
(b)   2
(c)   3

### QUESTION 9*

This and the next two questions are about the following situation:

A light ray is propagating within an optical fiber made from material with a high refractive index, n = 1.6, as shown in the figure. The fiber is surrounded by air, nair = 1.

What is the maximum angle θ through which the optical fiber may be bent before the light ray will exit the fiber?

(a)   42.1°
(b)   51.3°
(c)   58.6°

### QUESTION 10*

How does your answer change if the optical fiber is surrounded by water, nwater = 1.33 ?

(a)   33.8°
(b)   44.3°
(c)   50.9°

### QUESTION 11*

You would like to improve the performance of the optical fiber in water by encasing it in cladding with index of refraction, ncladding = 1.1. What is the new maximum bending angle?

(a)   40.8°
(b)   46.6°
(c)   65.4°

### QUESTION 12*

This and the next two questions are about the following situation:

An optical system consists of three parallel slabs, A, B, and C, in air, as shown in the figure. A ray of light that in vacuum has the wavelength 550 nm, is incident on the AB boundary, as shown. The refractive index of slab B is 2.4.

What is the wavelength of the light in slab B in nanometers?

(a)   550
(b)   447
(c)   352
(d)   229
(e)   195

### QUESTION 13*

When the incident angle θ is 60° it is found that the refracted angle Φ is 30°. What is the approximate refractive index of slab A?

(a)   1.1
(b)   1.4
(c)   1.7
(d)   2.7
(e)   2.9

### QUESTION 14*

When θ is increased to 70° it is found that total internal reflection occurs at the BC boundary. What is the refractive index of slab C?

(a)   1.0
(b)   1.3
(c)   1.4
(d)   1.7
(e)   2.1

### QUESTION 15*

This and the next three questions concern the following situation:

A lens forms an image of an object which is 30 cm in front of the lens. The image is 6 cm from the lens on the same side of the object, as indicated in the figure.

What is the focal length of the lens in centimeters?

(a)   -7.5
(b)   -5.0
(c)   +2.5
(d)   +5.0
(e)   +7.5

### QUESTION 16*

The lens is converging.

(T)   True
(F)   False

### QUESTION 17*

If the object is 10 cm in height, how high is the image in centimeters?

(a)   2
(b)   5
(c)   6
(d)   10
(e)   15

### QUESTION 18*

The image is inverted.

(T)   True
(F)   False

### QUESTION 19*

Two stars are photographed using a telescope with a circular aperture of diameter 2.44 m and light of wavelength 5 × 10-7 m. If both stars are 1020 m from us, what is their minimum separation such that we can recognize them as two stars (instead of just one)? Ignore any scattering of light in the atmosphere that might cause blurring.

(a)   a = 5.0 × 1013 m
(b)   a = 2.5 × 1013 m
(c)   a = 1.22 × 1014 m
(d)   a = 1.49 × 1014 m
(e)   a = 2.75 × 1015 m

### QUESTION 20*

Consider a diffraction pattern produced by passing light of wavelength λ though a screen containing a series of equally spaced slits.

The total number of slits is greater in the pattern on the right than in the pattern on the left.

(T)   True
(F)   False

### QUESTION 21*

This and the next question concern the following situation:

Reading glasses with a power of +2.0 diopters are used to help a far-sighted person see text as close as 35 cm in front of her eyes. Without the glasses, the closest she can see clearly is

(a)   0.66 m
(b)   1.17 m
(c)   1.53 m

### QUESTION 22*

These glasses would look most closely like which one of these figures

(a)   A
(b)   B

### QUESTION 23*

Light with a wavelength λ = 325 nm in air constructively-interferes from a thin plastic coating (n = 1.2) on a thick glass plate (n = 1.4). Find the minimum (non-zero) thickness of the coating.

(a)   135 nm
(b)   206 nm
(c)   315 nm
(d)   443 nm
(e)   586 nm

### QUESTION 24*

If the thick glass plate and thin plastic coating were submerged in water (n = 1.33), the answer to the previous problem (still assuming λ = 325 nm in air) would

(a)   change.
(b)   not change.

### QUESTION 25*

This and the next two questions are about the following situation:

Blue light with wavelength λ = 380 nm is incident upon two narrow slits separated by a distance d before striking a screen 5.2 meters away. The distance between the central bright fringe and first dark fringe is 1.8 × 10-3 m. Calculate d the spacing between the slits. (You may approximate sin(θ) ≈ tan(θ) ≈ θ.)

(a)   d = 0.15 mm
(b)   d = 0.21 mm
(c)   d = 0.36 mm
(d)   d = 0.41 mm
(e)   d = 0.55 mm

### QUESTION 26*

Now red light (λ = 650 nm) is incident on the same two slits, the distance y between the central bright fringe and the first dark fringe is

(a)   y < 1.8 mm
(b)   y = 1.8 mm
(c)   y > 1.8 mm

### QUESTION 27**

Now the two slits are replaced by a single slit with width w= d, and illuminated with the original blue light. What is the distance y to the first dark fringe?

(a)   y < 1.8 mm
(b)   y = 1.8 mm
(c)   y > 1.8 mm

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.