### Spring 2005 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 ***.

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 109. The exam period was 90 minutes; the mean was 77.7; the median was 81. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

This and the next question are about the following situation:

A double-slit experiment is set up as shown in the following figure. Light from a laser illuminates a pair of slits etched in an opaque barrier. The spacing between the slits is 10-4 m; the distance from the barrier containing the slits to a viewing screen is 2 m. Because of diffraction, a pattern of light and dark spots is seen on the viewing screen. The distance from the central bright spot to the first bright spots on either side is 10-2 m.

What is the wavelength of the laser light illuminating the pair of slits?

(a)   2.00 × 10-6 nm
(b)   107 nm
(c)   1.22 × 105 nm
(d)   500 nm
(e)   610 nm

### QUESTION 2*

If the wavelength of the laser light is increased by 50%, the spacing between the bright spots on the viewing screen will

(a)   increase by 100%.
(b)   increase by 50%.
(c)   remain unchanged.
(d)   decrease by 50%.
(e)   decrease by 100%.

### QUESTION 3*

This and the next question concern the following situation:

Two lenses are placed along a principal axis separated by 40 cm. The lens on the left in the figure below has a focal length of 10 cm while the lens on the right has a focal length of 20 cm. An object (the arrow) is placed 15 cm to the left of the first lens.

The two lens system forms an image of the arrow. Where is it?

(a)   10 cm to right of second lens
(b)   20 cm to left of second lens
(c)   3.33 cm to right of second lens
(d)   6.67 cm to left of second lens
(e)   3.33 cm to right of second lens

### QUESTION 4**

What is the total magnification of the two lens system?

(a)   MT = -4.0
(b)   MT = -2.0
(c)   MT = -1.67
(d)   MT = -1.33
(e)   MT = -1.0

### QUESTION 5**

Two laser beams, one red and the other blue propagate along the axis of a solid prism with a trapezoidal cross-section as shown in the figure below. The corner angle of the trapezoid is 60°. Inside the prism the index of refraction for red light is 1.49 and that for blue light is 1.52. Outside the prism there is a fluid that has an index of refraction equal to 1.33 for both red and blue light.

What is the angular separation between the red light and the blue light when the rays leave the prism?

(a)   1.043°
(b)   1.414°
(c)   1.733°
(d)   3.550°
(e)   7.272°

### QUESTION 6*

At one instant in time an electromagnetic wave traveling in space is found to have a magnetic field strength of 3.00 T. The strength of the wave's electric field at the same instant in time must be approximately

(a)   3.00 V/m.
(b)   9.00 × 108 V/m.
(c)   1.60 × 10-19 V/m.

### QUESTION 7**

Astronomers have determined that our universe is expanding: distant galaxies are found to be moving away from us at high speed. Because of this, light reaching Earth from these galaxies is Doppler shifted to shorter wavelengths.

(T)   True
(F)   False

### QUESTION 8**

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

Unpolarized light with intensity I0 is incident on a stack of three linear polarizers with transmission axis oriented as shown below.

Calculate I3, the intensity of the light transmitted by the entire stack of polarizers.

(a)   I3 = 0
(b)   I3 = 3I0 /32
(c)   I3 = 3I0 /16

### QUESTION 9**

If the magnetic field after passing through the first polarizer is B1, then what is the amplitude after passing through the third polarizer?

(a)   B3= 0.433 B1
(b)   B3= 0.500 B1
(c)   B3= 0.866 B1

### QUESTION 10**

If the middle polarizer is rotated from an angle of 30° down to an angle of 45°, the intensity of light transmitted by the entire stack will

(a)   decrease.
(b)   remain the same.
(c)   increase.

### QUESTION 11**

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

Two flat mirrors of width 2 m and height 2 m are attached to the front wall and left wall inside a room as shown in the Figure. The two mirrors are perpendicular to each other. An object of height 1 m is placed at location B, which is 1.6 m away from the left mirror and 0.8 m away from the front mirror.

How many images of object B (excluding the object itself) can be seen by a person (of normal height) standing at position A, which is 2 m away from both mirrors?

(a)   1
(b)   2
(c)   3

These images are

(a)   real.
(b)   virtual.

### QUESTION 13***

The person now walks to the right. How far can the person walk before one image becomes unobservable?

(a)   0.4 m
(b)   0.6 m
(c)   0.8 m
(d)   1.0 m
(e)   1.2 m

### QUESTION 14**

In bright light, the pupil in a cat's eye resembles a vertical slit, while that in a cow's eye is a horizontal slit, as shown in the figure.

If the shape of the animal's pupil plays a role in its visual acuity, which statement is true?

(a)   The cat's eye has better horizontal than vertical resolution, while the cow's eye has better vertical than horizontal resolution.
(b)   The cat's eye has better vertical than horizontal resolution, while the cow's eye has better horizontal than vertical resolution.
(c)   The vertical and horizontal resolutions of the cat's eye are nearly identical; the vertical and horizontal resolutions of the cow's eye are nearly identical.

### QUESTION 15*

A Chicago radio station broadcasts with frequency 93.1 MHz. The approximate wavelength of its signal is

(a)   2.79 × 1016 m.
(b)   3.22 m.
(c)   0.31 m.

### QUESTION 16**

This and the next question concern the following situation:

In the following circuit the frequency f is tuned to maximize the RMS current flowing through the resistor. (Recall that ω = 2πf.)

The correct value of f is

(a)   31.6 Hz
(b)   377 Hz
(c)   5033 Hz

### QUESTION 17*

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

A mirror is made by spraying reflector paint on the inside of a portion of the surface of a sphere as shown. The location of the center of this sphere is indicated. An image (either real or virtual) of the object in the figure may be formed by this mirror. Assume that the approximations for an ideal concave mirror are valid (i.e., the rays make small angles with the optical axis).

In which region will this image be located?

(a)   region I (to the left of the center of curvature)
(b)   region II (between the center of curvature and the focus)
(c)   region III (between the focus and the surface of the mirror)
(d)   region IV (to the right of the mirror)
(e)   No image is formed.

### QUESTION 18*

Is the image up-side down?

(a)   Yes
(b)   No

### QUESTION 19*

What is the magnitude of the magnification?

(a)   |m| = 1
(b)   |m| < 1
(c)   |m| > 1

### QUESTION 20***

Six slits are cut into an opaque screen as shown in the following figure. The spacing between the slits is not uniform; the y positions of the slits are indicated on the diagram. A viewing screen is positioned several meters to the right of the slits.

The screen is illuminated from the left by a light source of wavelength λ. The particular light rays leaving the slits and converging at one point on the viewing screen are drawn in the diagram. The path lengths from the slits to that point on the screen differ for each of the rays. (The path length differences relative to the top-most ray are shown in the figure.)

The intensity of the light measured at the point of convergence of the rays is I6. After the measurement is made, all but one of the slits are covered and an intensity I1 is measured. What is the ratio of the intensities I6 / I1 ?

(a)   I6 / I1 = 0
(b)   I6 / I1 = 2
(c)   I6 / I1 = 4
(d)   I6 / I1 = 9
(e)   I6 / I1 = 36

### QUESTION 21*

This and the next question concern the following situation:

An object (another arrow!) is placed 30 cm behind a lens with focal length of 20 cm.

The image that is formed is

(a)   upright and enlarged.
(b)   inverted and enlarged.
(c)   inverted and smaller.

### QUESTION 22*

What is the magnification of the image in this situation?

(a)   +4
(b)   +2
(c)   +1
(d)   -2
(e)   -4

### QUESTION 23*

Which one of the spherical mirrors below would cause light from a distant object on the left-hand side of the mirror to form a virtual image on the right-hand side?

(a)
(b)

### QUESTION 24*

Light passes from material 2 into material 1 along the rays indicated in the figure to the right. Which one of the following is true?

(a)   n2 > n1
(b)   n2 < n1

### QUESTION 25**

This and the next question are about the following situation:

Two parallel rays propagating parallel to the principal axis enter a two lens system as shown above. The separation between the two rays entering the first lens is 0.5 cm. The first lens has focal length 10 cm, while the second lens has an unknown focal length. In addition the separation between the two lenses is not known, except that it is greater than 10 cm. When the light leaves the second lens the rays are parallel and propagate parallel to the principal axis, now separated by 1.0 cm.

The lenses are separated by:

(a)   (f1+f2)/2
(b)   (f1+f2)
(c)   2(f1+f2)

### QUESTION 26**

What is the focal length of the second lens?

(a)   2.5 cm
(b)   5.0 cm
(c)   10.0 cm
(d)   14.14 cm
(e)   20.0 cm

### QUESTION 27*

An anti-reflective coating can be used to reduce the amount of light bouncing off the surface of a camera lens. A hypothetical example of this is shown in the following figure, in which the thickness of the coating is t. Note the indices of refraction of the coating and the glass lens.

Green light of wavelength λ = 560 nm is normally incident on the lens. In order to minimize reflections from the front of the lens, the thickness of the coating should be

(a)   t = 1.22 nm
(b)   t = 108 nm
(c)   t = 280 nm
(d)   t = 560 nm
(e)   t = 1120 nm

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.