### Fall 2007 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 96. The exam period was 90 minutes; the mean was 78.3; the median was 81. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

• A reminder about prefixes: p (pico) = 10-12; n (nano) = 10-9; μ (micro) = 10-6; m (milli) = 10-3; k (kilo) = 10+3; M or Meg (mega) = 10+6; G or Gig (giga) = 10+9.

### QUESTION 1*

This and the next two questions concern the following situation:

A ray of red light passes through a prism. The trajectory is such that the ray is horizontal when inside the prism. The index of refraction n of the prism is 1.517 at the wavelength of red light.

At what angle α does the ray enter the prism?

(a)   0°
(b)   19°
(c)   30°
(d)   49°
(e)   60°

### QUESTION 2*

The exit angle β below the horizon obeys:

(a)   β < α
(b)   β = α
(c)   β > α

### QUESTION 3*

A ray of blue light, for which the index of refraction of the prism is n = 1.538, traveling the horizontal path inside the prism will be refracted

(a)   below the ray of red light.
(b)   at the same trajectory as the ray of red light.
(c)   higher than the ray of red light.

### QUESTION 4*

A laser beam travels from an area of unknown material (n2 = ?) into an area of water (n1 = 1.3). What is the minimal refractive index of the unknown material (n2) such that a ray hitting the interface at an angle θ = 48° to the normal will be totally reflected?

(a)   1.15
(b)   1.5
(c)   1.75
(d)   2
(e)   2.5

### QUESTION 5*

This and the next question are related.

A woman is staring at the back (the convex side) of a spoon, at a distance much larger than the spoon's radius of curvature. The image of the woman's face is:

(a)   reduced, real, inverted
(b)   reduced, virtual, upright
(c)   magnified, real, upright

### QUESTION 6*

The woman now stares at the front (the concave side) of the spoon from the same distance. The image of the woman's face is:

(a)   reduced, real, inverted
(b)   reduced, virtual, upright
(c)   magnified, real, upright

### QUESTION 7*

An elegant man is getting dressed in front of a mirror. The man's eyes are at a height h = 170 cm above the floor. The horizontal distance between the man and the mirror is x = 200 cm. The vertical size of the mirror is m = 45 cm.

What is the maximum height y above the floor the mirror can be placed, so that the man can still see his shoes in the mirror?

(a)   0 cm
(b)   13.5 cm
(c)   45 cm
(d)   85 cm
(e)   100 cm

### QUESTION 8*

This and the next three questions concern the following situation:

A lady bug of height 0.5 cm is placed 5 cm away from a converging lens. The focal distance of the lens is 12 cm.

At what distance from the lady bug will its image appear?

(a)   7.6 cm left of the lady bug
(b)   3.6 cm to the left of the lady bug
(c)   5 cm to the right of the lady bug
(d)   7.6 cm to the right of the lady bug
(e)   at infinity

### QUESTION 9*

What will be the height of the image?

(a)   0.05 cm
(b)   0.5 cm
(c)   0.86 cm

The image is:

(a)   upright
(b)   inverted

The image is:

(a)   real
(b)   virtual

### QUESTION 12*

This and the next question concern the following situation:

An object is placed 20 cm to the left of a 2-lens system of convex lenses. The left lens has a focal length f1 = 12 cm. The right lens has a focal length f2 = 18 cm. The lenses are 40 cm apart.

Where is the final image located?

(a)   30 cm right of lens #1
(b)   22.5 cm left of lens #2
(c)   22.5 cm right of lens #1
(d)   15 cm right of lens #2
(e)   at infinity

### QUESTION 13*

What is the total magnification of the 2-lens system?

(a)   -3.38
(b)   -2.25
(c)   -1.5
(d)   2.25
(e)   3.38

### QUESTION 14*

This and the next question concern the following situation:

Initially unpolarized light is incident on a series of two linear polarizers.

If the initial intensity of the incident (unpolarized) light is I0, what is the intensity I2 transmitted by the stack?

(a)   I2 = 0.015 I0
(b)   I2 = 0.0301 I0
(c)   I2 = 0.48 I0

### QUESTION 15*

If the magnetic field amplitude after passing through the first polarizer is B1, what is the magnetic field amplitude B2 after passing through the second polarizer?

(a)   B2 = 0.0251 B1
(b)   B2 = 0.1736 B1
(c)   B2 = B1

### QUESTION 16*

This and the next question concern the following situation:

Electromagnetic waves of frequency 4 × 106 Hz and average energy density 1.5 × 10-6 J/m3 traveling in a vacuum are incident upon a panel of area 12 m2.

What is the wavelength of these waves?

(a)   1.33 × 10-2 m
(b)   75 m
(c)   1.2 × 1015 m

### QUESTION 17**

How much energy is transmitted through the panel in a period of 15 s?

(a)   5.4 × 103 J
(b)   8.1 × 104 J
(c)   3.2 × 105 J

### QUESTION 18**

Blue light travels through glass ___________ red light.

(a)   faster than
(b)   at the same speed as
(c)   slower than

### QUESTION 19**

Light passes down through three layers of transparent materials each with a different index of refraction as shown. At which interface is total internal reflection possible?

(a)   A (from n=1.3 to n=1.4)
(b)   B (from n=1.4 to n=1.2)

### QUESTION 20**

This and the next question concern the following situation:

A film of oil of thickness t is floating on water. The index of refraction is 1.0, 1.45 and 1.33 for air, oil and water, respectively. A person views the film from the air in a direction normal to the surface.

The person sees that there is constructive interference of reflected light of wavelength 630 nm. What is the minimum thickness t of the oil film?

(a)   109 nm
(b)   218 nm
(c)   436 nm

### QUESTION 21*

The person sees that there is destructive interference of reflected light of wavelength 450 nm. What is the minimum thickness t of the oil film?

(a)   155 nm
(b)   225 nm
(c)   310 nm

### QUESTION 22**

A person with a pupil diameter of 2.5 mm views the headlights of a distant car. Assume that the headlights are separated by a distance of 1.2 m, and emit light at just one wavelength of 550 nm. What is the distance of the car from the person if the person can just barely resolve the two headlights?

(a)   4,470 m
(b)   5,500 m
(c)   12,600 m

### QUESTION 23*

This and the next question concern the following situation:

For a wavelength of 440 nm, a diffraction grating produces a 2nd-order bright fringe at an angle of 28°.

What is the slit spacing of the grating?

(a)   937 nm
(b)   1,870 nm
(c)   3,749 nm

### QUESTION 24*

For an unknown wavelength, the same grating produces a 2nd-order bright fringe at an angle of 42°. What is the unknown wavelength?

(a)   308 nm
(b)   314 nm
(c)   627 nm

### QUESTION 25*

This and the next two questions concern the following situation:

A double-slit experiment is set up using red light with a wavelength of 633 nm. The slits are separated by a distance of 0.075 mm. The interference pattern is viewed on a screen 1.8 m away from the slits.

What is the distance between two adjacent bright fringes on the screen?

(a)   1.52 cm
(b)   1.69 cm
(c)   3.04 cm

### QUESTION 26**

What is the difference in the distance traveled by the rays from the top and bottom slit reaching the third order bright fringe on the screen?

(a)   633 nm
(b)   950 nm
(c)   1899 nm

### QUESTION 27**

A single slit of width 0.075 mm, illuminated by light of wavelength 633 nm, yields a diffraction pattern on a screen 1.8 m away. What is the distance between the central bright fringe and the second order dark fringe on the screen?

(a)   1.5 cm
(b)   1.7 cm
(c)   3.0 cm

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.