### Summer 2000 Physics 102 Hour Exam 3(20 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 20 questions; two-choice questions are worth 2 points each, three-choice questions are worth 3 points each, five-choice questions are worth 6 points each. The maximum possible score is 93. When the exam was given, the minimum "A" score was 76; the minimum "B" was 67; the minimum "C" was 48; the minimum "D" was 31. The mean was 62.7; the median was 67. Click here to see formula sheet 1, formula sheet 2 that came with the exam.

### QUESTION 1*

Light from an UNPOLARIZED source is incident on 3 polarizing sheets as shown. The polarization axes of the 3 sheets make angles q1, q2, and q3 with respect to the vertical, as shown. For which combination of angles will the light emerging from the third sheet have the greatest intensity?

(a)   q1 = 0; q2 = 0; q3 = 90°
(b)   q1 = 0; q2 = 90°; q3 = 90°
(c)   q1 = 90°; q2 = 0; q3 = 90°
(d)   q1 = 0; q2 = 45°; q3 = 90°
(e)   q1 = 30°; q2 = 60°; q3 = 90°

### QUESTION 2**

Light from a HORIZONTALLY POLARIZED source is incident on 3 polarizing sheets as shown. The polarization axes of the 3 sheets make angles q1, q2, and q3 with respect to the vertical, as shown. For which combination of angles will the light emerging from the third sheet have the greatest intensity?

(a)   q1 = 0; q2 = 0; q3 = 90°
(b)   q1 = 0; q2 = 90°; q3 = 90°
(c)   q1 = 90°; q2 = 0; q3 = 90°
(d)   q1 = 0; q2 = 45°; q3 = 90°
(e)   q1 = 30°; q2 = 60°; q3 = 90°

### QUESTION 3***

A person has defective eyes so that he cannot read a book when it is closer than 120 cm. What is the focal length of the lenses in the eyeglasses that should be prescribe to solve this deficiency so that he can read a book at the normal distance of 25 cm?

(a)   95 cm
(b)   32 cm
(c)   21 cm
(d)   -21 cm
(e)   -32 cm

### QUESTION 4***

In a 2 slit interference experiment, the slits are illuminated with a mixture of red, blue, and green light.

(a)   The first-order maximum of green light appears closer to the central maximum than that of blue light.
(b)   The first-order maximum of green light appears further from the central maximum than that of red light.
(c)   The first-order maximum of green light appears closer to the central maximum than that of red light.
(d)   (a) and (b) are both correct statements.
(e)   (b) or (c) depending on the separation between the slits

### QUESTION 5***

A lens focusses parallel rays of light to a spot that is FL away from the lens. A mirror focusses parallel rays of light to a spot that is FM away from the mirror. When the lens (index of refraction = 1.5 ) and the mirror are in air, FL = FM. The lens and the mirror are then (separately) immersed in water (index of refraction = 1.33). How, if at all, are these distances changed?

(a)   FL and FM are not changed.
(b)   They change, but FL is still the same as FM.
(c)   FL increases but FM does not change.
(d)   Both increase, but FL increases more.
(e)   FL decreases, but FM does not change.

### QUESTION 6**

This and the next two questions pertain to the following situation:

A mirror is made by spraying reflecting paint on the inside of a portion of the surface of a sphere as shown above. The location of the center of the sphere is indicated. An image (either real or virtual) of the object shown may be formed by the mirror. (Regions II and III have the same length.)

The image is located in region:

(a)   I
(b)   II
(c)   III
(d)   IV
(e)   II or III

The image is:

(a)   real
(b)   virtual

The image is:

(a)   upright
(b)   inverted

### QUESTION 9*

An astronomer photographs stars in the sky with a camera in which the light must pass through a narrow rectangular slit before it reaches the film. The film is sensitive to light of wavelength 500 nm and the width of the slit is 1 mm. About how close can 2 stars be located in the sky and still be recognized as two stars and not one? Assume that the two stars are both 3x1017 m from the earth. (Note that for small angles sin q » tan q » q in radians.)

(a)   1.5 × 107 m apart
(b)   1.5 × 1010 m apart
(c)   1.5 × 1012 m apart
(d)   1.5 × 1014 m apart
(e)   1.5 × 1016 m apart

### QUESTION 10*

This and the next question pertain to the following situation:

Monochromatic light is incident upon two narrow slits separated by a distance d = 2.3 x 10-3 m before striking a screen 4.3 meters away. The distance between the central and first bright fringe is 1.1 ´ 10-3 m. (You may approximate sin(q) » tan(q) » q .)

Calculate the wavelength of the light.

(a)   l = 588 nm
(b)   l = 550 nm
(c)   l = 444 nm

### QUESTION 11*

The entire apparatus is placed in a tank of water (n=1.33). The spacing Dx on the screen between the first two dark fringes

(a)   increases.
(b)   decreases.
(c)   remains the same.

### QUESTION 12*

This and the next two questions pertain to the following situation:

In the figure are shown two lenses. The focal length f1 is unknown, but f2 = 12 cm. The lenses are separated by 30 cm. When an object 1 cm high is located 4 cm to the left of the first lens, it produces an image (not drawn) 12 cm to the right of the first lens. (Note: DRAWING IS NOT TO SCALE!)

Find f1 the focal length of the first lens.

(a)   f1 = +3.33 cm
(b)   f1 = +3.00 cm
(c)   f1 = -6.00 cm

### QUESTION 13*

Find d2 the position the image formed by the second lens, expressed as a distance from the second lens.

(a)   d2 = 36 cm
(b)   d2 = 120 cm
(c)   d2 = 210 cm

### QUESTION 14*

What is h2 the height of the image formed by the second lens?

(a)   h2 = 6 cm
(b)   h2 = 14 cm
(c)   h2 = 28 cm

### QUESTION 15**

This and the next two questions pertain to the following situation:

A person standing on the bank at the edge of a pond sees a fish beneath the surface as shown in the figure. Note that certain distances and the angle f (measured from the horizontal) for the line of sight at which the fish is seen are given. The surface of the bank can be considered to be level with the surface of the pond. The index of refraction of the water is 1.3. (Note: DRAWING IS NOT TO SCALE!)

What is the true depth of the real fish beneath the surface?

(a)   2.5 m
(b)   3.6 m
(c)   4.5 m
(d)   5.6 m
(e)   7.8 m

### QUESTION 16***

At what height above the surface of the bank do the eyes of the person appear to be as seen by the fish? (Note that the eyes are displaced only toward the top or the bottom of the paper from their true location.)

(a)   2.5 m
(b)   3.6 m
(c)   4.5 m
(d)   5.6 m
(e)   7.8 m

### QUESTION 17***

If the fish gets close enough to the surface, the person will no longer be able to see it because of the phenomenon of total internal reflection.

(T)   True
(F)   False

### QUESTION 18**

This and the next question pertain to the following situation:

Two thick glass plates (with index of refraction n = 1.5 are separated by a distance s as shown in the figure below. Light of wavelength l = 560 nm (in vacuum) is constructively reflected when illuminated perpendicularly from above. Initially the gap between the plates is filled with air (n = 1.0).

What is the minimum separation, s, for which this constructive interference can occur.

(a)   93 nm
(b)   100 nm
(c)   140 nm
(d)   186 nm
(e)   280 nm

### QUESTION 19*

If the air between the plates is replaced by a liquid whose index of refraction is n = 1.4, find the smallest separation, s¢, for which constructive interference will now occur.

(a)   93 nm
(b)   100 nm
(c)   140 nm
(d)   186 nm
(e)   280 nm

### QUESTION 20**

Monochromatic light of wavelength 550 nm is incident on a single slit of width w and produces a diffraction pattern on a screen 5.0 meters away. The distance between the first and second dark fringes is 7.5 ´ 10-3 m as shown in the figure to the right. In the following you may assume that the angles locating the fringes are small (sinq » tanq » q).

Calculate w, the width of the slit:

(a)   w = 0.18 mm
(b)   w = 0.37 mm
(c)   w = 0.55 mm
(d)   w = 0.73 mm
(e)   w = 0.80 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.