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.

Some helpful information: • 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}.

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

(T) True (F) False

(a) 17 cm (b) 12 cm (c) 9.2 cm

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°

(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.

(a) (b) (c)

(a) 4 cm (b) 9 cm (c) 20 cm

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

(a) behind (b) in front of

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°

(a) largest (b) smallest

The upward-pointing arrow is a real object held 11 cm in front of a lens of focal length f_{1} = 10 cm. A second lens, of focal length f_{2} =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

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°

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

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

Unpolarized light of intensity 15 W/m^{2} 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/m^{3} (b) 15 J/m^{3} (c) 4.5 × 10^{-9} J/m^{3}

(a) 3.1 W/m^{2} (b) 4.4 W/m^{2} (c) 5.7 W/m^{2} (d) 8.8 W/m^{2} (e) 11.5 W/m^{2}

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

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

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