### Fall 2003 Physics 102 Hour Exam 3(28 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 28 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 122. The exam period was 90 minutes; the mean was 104.8; the median was 108. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

Shown here are three ray tracing diagrams. Which one is not correct?

(a)
(b)
(c)

### QUESTION 2*

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

An object of 2 cm height is at a position 6 cm away from a spherical concave mirror. The radius of curvature of the mirror is 8 cm. The locations of the center of curvature (C) and the focal point (F) are indicated.

How far is the image from the mirror?

(a)   4 cm
(b)   6 cm
(c)   8 cm
(d)   10 cm
(e)   12 cm

### QUESTION 3*

What is the size of the image?

(a)   1 cm
(b)   2 cm
(c)   4 cm
(d)   8 cm
(e)   16 cm

### QUESTION 4*

The image is

(a)   upright relative to the object.
(b)   inverted relative to the object.

The image is

(a)   real.
(b)   virtual.

### QUESTION 6*

If the object is moved closer to the focal point (but still to the left of the focal point), the image moves

(a)   closer to the mirror.
(b)   farther from the mirror.

### QUESTION 7**

Where must one place the object such that the object and the image are the same distance to the left of the mirror?

(a)   at point F.
(b)   at point C.
(c)   such a point does not exist.

### QUESTION 8*

If the object is moved between the focal point and the mirror, the image is

(a)   real.
(b)   virtual.

### QUESTION 9*

An optical fiber is made of a central region with index of refraction 1.5, surrounded by a surface coating of index of refraction 1.45. The fiber is surrounded by air with index 1.0. The angle θ is the angle of a ray of light in the fiber, measured with respect to the horizontal (which is the axis of the fiber).

What is the maximum value of θ for which no light emerges into the air outside the fiber?

(a)   38.6°
(b)   48.2°
(c)   53.6°
(d)   63.5°
(e)   70.1°

### QUESTION 10*

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

A person 2 m high stands at the edge of a swimming pool 3 m deep, looking for a lost watch on the bottom of the pool. The watch is located a distance x from the edge of the pool. The actual ray which travels from the watch to the person’s eye emerges from the water 1m from the edge of the pool. See the figure.

Find the angle θ. This is the angle between the ray emerging in air and the normal to the pool surface.

(a)   10.3°
(b)   23.2°
(c)   26.6°
(d)   31.4°
(e)   46.2°

### QUESTION 11**

Find the distance x. This is the actual distance of the watch away from the edge of the pool.

(a)   0.82 m
(b)   1.69 m
(c)   2.07 m
(d)   3.61 m
(e)   4.34 m

### QUESTION 12*

Find the distance x'. This is the apparent distance of the watch from the edge of the pool

(a)   2.5 m
(b)   5.0 m
(c)   7.5 m

### QUESTION 13*

A thin layer of magnesium fluoride (MgF2) with an index of refraction of 1.38 coats a piece of glass with index of refraction of 1.5. Light with a wavelength (in air) of 532 nm strikes the MgF2 surface from above at normal incidence.

What thickness should the MgF2 layer be in order to make an anti-reflection (AR) coating, so that none of the 532 nm light is reflected from the surface? An AR coating requires destructive interference between the light reflected from the air / MgF2 interface and light reflected from the MgF2 / glass interface.

(a)   12 nm
(b)   250 nm
(c)   45 nm
(d)   120 nm
(e)   96 nm

### QUESTION 14*

A prism has one side vertical and the other at an angle of 20° to the vertical as shown in the figure. The glass of which the prism is made has index of refraction n = 1.50.

Light is incident from the horizontal direction. It goes through the prism and emerges back into air, at an angle θ, measured with respect to the normal of the second surface of the prism. Find θ.

(a)   19.4°
(b)   23.0°
(c)   27.3°
(d)   30.9°
(e)   33.5°

### QUESTION 15*

This and the next question concern the following situation:

An object is placed an unknown distance (x cm) in front of a convex mirror with a focal length f = -8 cm. The locations of the focal point (F) and the center of curvature (C) are shown.

The image is always

(a)   closer to the mirror than the object.
(b)   farther from the mirror than the object.

### QUESTION 16**

For what distance x will the image be one third the size of the object?

(a)   6 cm
(b)   8 cm
(c)   10 cm
(d)   12 cm
(e)   16 cm

### QUESTION 17**

Light with wavelength λ is emitted from point A and travels to point B, as in the figure above. The light takes two paths: one straight from A to B, and another path where the light bounces off of a piece of glass with index of refraction 1.5.

What is the correct equation to use for destructive interference between the two paths? In these equations, m is an integer.

(a)   2 r – L = mλ
(b)   2 r – L = (m+1/2) λ

### QUESTION 18*

This and the next two questions concern the following situation:

Two lenses are separated by 16 cm. Both Lens #1 and Lens #2 are converging lenses and have a focal length of 5 cm. An object (arrow) is located 10 cm to the left of Lens #1.

If lens #2 were not present, the image formed by lens #1 would be

(a)   5 cm to the right of lens #1.
(b)   10 cm to the right of lens #1.
(c)   15 cm to the right of lens #1.
(d)   20 cm to the right of lens #1.
(e)   25 cm to the right of lens #1.

### QUESTION 19*

Where is the final image of the pair of lenses?

(a)   25 cm to the left of lens #2
(b)   15 cm to the left of lens #2
(c)   10 cm to the left of lens #2
(d)   20 cm to the right of lens #2
(e)   30 cm to the right of lens #2

### QUESTION 20*

The final image formed by the pair of lenses is

(a)   inverted relative to the object.
(b)   upright relative to the object.

### QUESTION 21*

This and the next question concern the following situation:

A glass cell filled with a gas of atoms emits light onto a diffraction grating, as in the diagram below. The screen is 1 m from the grating, and the bright fringes are used to identify the atoms in the gas and to learn about the electronic structure of the atoms.

A grating with 1200 lines/cm is used, and the first order bright fringe appears at a distance y = 9.4 cm above the center of the screen. If Cs atoms emit light at 852 nm, Rb atoms at 780 nm, and Na atoms at 589 nm, which type of atom is in the glass cell?

(a)   Cs
(b)   Rb
(c)   Na

### QUESTION 22*

Now a grating with 4000 lines/cm is used, and we find that actually two wavelengths are being emitted from the atoms, even though there is only one type of atom in the cell. One first order bright fringe appears at y = 32.839 cm and the other at y = 33.541 cm. What is the difference in wavelength between the two types of light emitted from the gas? Do not use the small angle approximation.

(a)   8.2 nm
(b)   15 nm
(c)   42 nm
(d)   0.35 nm
(e)   78 nm

### QUESTION 23*

This and the next question concern the following situation:

Light with wavelength 633 nm from a laser is incident on a slit with diameter 1 cm. The light is projected onto a special mirror designed by Jim Faller that was left on the moon 3.77x108 m away from the slit by astronauts.

Which one of the following diagrams best represents the intensity profile of the light at the moon?

(a)
(b)
(c)

### QUESTION 24**

The width of the laser beam at the moon is determined by the distance between the two first dark fringes which are to either side of the central maximum. What is the width of the beam at the moon?

(a)   1.0 μm
(b)   48 km
(c)   1.0 cm
(d)   56 km
(e)   1.0 m

### QUESTION 25*

This and the next question are about the following situation:

Electromagnetic waves with a 517 m wavelength are emitted in phase from two radio towers that are 3 km apart as in the figure below. The radio towers are located at points D and E, and someone is trying to pickup the radio station at point A.

The reception will be best when the transmissions from D and E constructively interfere at A. For what minimum distance y greater than zero does this occur?

(a)   1.75 km
(b)   2.07 km
(c)   0.95 km

### QUESTION 26**

Now someone trying to jam the reception sets up another, stronger transmitter at F operating in phase with D and E, as in the figure below. Constructive interference of the D and E transmissions will occur at the point marked with a star. What should be the minimum distance x so that the broadcast from F destructively interferes (at the star) with the transmissions from D and E?

(a)   259 m
(b)   3.04 m
(c)   117 m
(d)   890 m
(e)   1000 m

### QUESTION 27*

This and the next question are about the following situation:

Two flat pieces of quartz are separated by an air gap of width d. Light from a laser with a 780 nm wavelength (in air) travels in the quartz and hits the quartz/air interfaces at normal incidence.

Which of the following is the minimum separation d for which the light reflected from the two quartz/air surfaces will destructively interfere?

(a)   187 nm
(b)   390 nm
(c)   125 nm
(d)   893 nm
(e)   795 nm

### QUESTION 28*

Now the space between the quartz is filled with zinc selenide, which has an index of refraction of 2.53. Which is the minimum separation d for which the light reflected from the two quartz/air surfaces will constructively interfere?

(a)   77 nm
(b)   12 nm
(c)   130 nm
(d)   250 nm
(e)   170 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.