### Summer 2008 Physics 102 Hour Exam 3(23 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 84. The exam period was 60 minutes; the mean was 66.8; the median was 61. 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:

Suppose you are capable of focusing on objects no closer than 40 cm from your eyes and no farther than 110 cm from them. To improve your vision, you will need separate prescriptions, one to correct for nearsightedness, and the other to correct for farsightedness.

You should assume that the weakest possible lens is prescribed to correct each problem.

Which focal length would be prescribed so that you could read a book held 22 cm from your eyes?

(a)   63 cm
(b)   49 cm
(c)   27.5 cm
(d)   22 cm
(e)   14 cm

### QUESTION 2*

To achieve normal vision, you will also need a prescription with a focal length f = -110 cm.

(T)   True
(F)   False

### QUESTION 3**

Assuming again you have uncorrected vision, hold (right up against your eye) a magnifying glass with focal length f = 12 cm. How close to this magnifying glass can you hold an object and still focus on it?

(a)   17 cm
(b)   12 cm
(c)   9.2 cm

### QUESTION 4**

This and the next question concern the following situation:

The picture shows light entering a glass prism normally from the right. You may assume this light is parallel to the bottom and top edges of the prism. The left edge of the prism makes an angle θ with respect to the bottom edge. The prism has an index of refraction n = 1.48 and is surrounded by air.

If θ = 68°, find Φ, the angle the emerging light makes with respect to the surface of the prism.

(a)   68°
(b)   56°
(c)   34°

### QUESTION 5***

For what range of angles θ will light emerge on the left side of the prism?

(a)   only for angles θ larger than 47.5°
(b)   only for angles θ smaller than 47.5°
(c)   only for angles θ larger than 42.5°
(d)   only for angles θ smaller than 42.5°
(e)   Light emerges regardless of the angle θ.

### QUESTION 6**

Rays of light pass through a lens as shown. Three points on the principal axis are identified. Of the three points shown, only one could plausibly be a focal point of the lens. Which could possibly be a focal point?

(a)
(b)
(c)

### QUESTION 7**

A real object of height 5 cm produces a virtual image of height 7.5 cm in a mirror of focal length f = 12 cm. How far in front of that mirror is the object being held?

(a)   4 cm
(b)   9 cm
(c)   20 cm

### QUESTION 8**

This and the next question concern the following situation:

A thin, spherical glass bowl is silvered on its outside to form a convex mirror. Its radius of curvature is 14 cm. A separate lens (not shown) focuses light onto a point 3 cm behind that mirror. In the diagram, "behind the mirror" implies to the right of that mirror.

Where does the mirror form an image of that light?

(a)   5.25 cm away from that mirror
(b)   3.8 cm away from that mirror
(c)   2.1 cm away from that mirror

### QUESTION 9**

Does the image form behind that mirror or in front of (to the left of) the mirror?

(a)   behind
(b)   in front of

### QUESTION 10*

This and the next question concern the following situation:

Light enters a glass slab (index of refraction n = 1.52) from the air at some angle θ. Inside the glass, it travels towards a boundary with water (index of refraction n = 1.33).

What angle θ corresponds to the critical angle for light within glass incident on the boundary to water?

(a)   43°
(b)   47°
(c)   49°

### QUESTION 11**

Is the angle above the largest angle θ (in air) at which light going from air into glass can escape from the glass into the water? Or is it the smallest such angle?

(a)   largest
(b)   smallest

### QUESTION 12**

This and the next two questions concern the following situation:

The upward-pointing arrow is a real object held 11 cm in front of a lens of focal length f1 = 10 cm. A second lens, of focal length f2 =15 cm, sits 12 cm away from a screen. Light passing from the object through those two lenses forms an image on the screen. How far apart are the two lenses?

(a)   20 cm
(b)   50 cm
(c)   98 cm
(d)   110 cm
(e)   170 cm

### QUESTION 13*

The final image formed on the screen is real.

(T)   True
(F)   False

### QUESTION 14***

The final image formed on the screen is inverted (an arrow pointing downward).

(T)   True
(F)   False

### QUESTION 15*

This and the next question concern the following situation:

A diffraction grating has 1650 lines (slits) per cm.

When illuminated by light of wavelength 540 nm, at which of these angles is the first-order maximum detected?

(a)   5°
(b)   7°
(c)   9°

### QUESTION 16**

The same diffraction grating is illuminated by light of wavelength 650 nm. What is the largest order maximum observable?

(a)   None are present other than the central maximum.
(b)   4th
(c)   9th

### QUESTION 17**

A single slit of width a = 0.08 mm is illuminated by light of wavelength 620 nm. The resulting pattern is projected onto a screen L = 2.7 m away. How far from the brightest point on the diffraction pattern is the second diffraction minimum?

(a)   3.1 cm
(b)   4.2 cm
(c)   5.2 cm
(d)   8.4 cm
(e)   10.4 cm

### QUESTION 18*

This and the next two questions concern the following situation:

Unpolarized light of intensity 15 W/m2 is incident on linear polarizer, oriented so that its transmission axis is vertical.

What is the (average) energy density of this light before it strikes the polarizer?

(a)   5 × 10-8 J/m3
(b)   15 J/m3
(c)   4.5 × 10-9 J/m3

### QUESTION 19*

Having passed through that vertically-oriented polarizer, the light strikes a second polarizer, whose transmission axis is 40° away from vertical. What is the intensity of light emerging from that second polarizer?

(a)   3.1 W/m2
(b)   4.4 W/m2
(c)   5.7 W/m2
(d)   8.8 W/m2
(e)   11.5 W/m2

### QUESTION 20***

It is possible to increase the intensity of light emerging from that second polarizer by inserting a third polarizer, suitably oriented, between the first two.

(T)   True
(F)   False

### QUESTION 21*

The protein shell of a particular virus has a diameter of 100 nm. This virus sits 1 cm beneath a microscope of aperture diameter 15 mm. What wavelength of radiation would just suffice to resolve opposite ends of this protein shell?

(a)   0.12 nm
(b)   1.2 nm
(c)   12 nm
(d)   120 nm
(e)   1200 nm

### QUESTION 22**

This and the next question concern the following situation:

A thin film of oil (index of refraction n = 1.4) is poured over glass (n = 1.5). Light of wavelength 480 nm shines down onto this oil from the air above it. What thinnest coating of oil will suffice to eliminate the reflections of that light?

(a)   42.9 nm
(b)   60 nm
(c)   85.7 nm
(d)   120 nm
(e)   171.4 nm

### QUESTION 23**

This same oil is now poured over water (n = 1.33). Call the thickness of this oil layer t. For which of the following values of t will light of 520 nm not be strongly reflected?

(a)   278.6 nm
(b)   371.4 nm
(c)   464.3 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.