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 116. The exam period was 90 minutes; the mean score was 94.2; the median was 98. 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}.

An optical fiber consists of a small cylinder of glass called the core, shown in gray, surrounded by a layer of glass called the cladding. Light rays entering the fiber propagate as shown. The index of refraction of the core is n = 1.444 . The intensity of the light in the fiber is 1.3 × 10^{8} W/m^{2}.

If the maximum angle off-axis θ with which a ray can propagate in the fiber is 4°, what is the index of refraction of the cladding?

(a) 1.44 (b) 1.53 (c) 1.71

(a) 2.3° (b) 4.0° (c) 5.8°

(a) 10 mW (b) 40 mW (c) 62 mW

(a) 1.2 × 10^{8} m/s (b) 2.1 × 10^{8} m/s (c) 4.3 × 10^{8} m/s

(a) half the height (b) ¾ of the height (c) same height (d) slightly longer than the height (e) twice the height

(a) 13.1° (b) 51.6° (c) 63.4° (d) 78.5° (e) 84.2°

(a) -20 diopters (b) -5 diopters (c) 0.05 diopters (d) 5 diopters (e) 20 diopters

Two lenses are indicated below. The convex lens has a focal length of 11 cm and the concave lens has a focal length of -17 cm. The object is located 14.1 cm to the left of the convex lens.

Where is the final image located with respect to the concave lens? Standard sign conventions apply.

(a) -10.1 cm (b) 24.3 cm (c) 32.0 cm (d) 44.9 cm (e) 60.4 cm

(a) upright. (b) inverted.

A sodium light bulb is analyzed with a diffraction grating. The slits of the grating have a separation of 1000 nm. The sodium light has two closely spaced emission lines, whose wavelengths are 589.0 nm and 589.6 nm.

What is the angle Δθ between the first-order maxima corresponding to 589.0 nm and the first-order maxima of 589.6 nm?

(a) 0° (b) 0.043° (c) 0.31° (d) 4.3° (e) 36.2°

(a) 45.3° (b) 65.9° (c) There is no second-order maximum.

A vertically polarized beam of light goes through a system of 5 polarizers. The first polarizer is oriented at 18° from the vertical, and the transmission axis of each successive polarizer is oriented 18° from the previous one.

The emerging beam from the five polarizers has an intensity of 30 W/m^{2}. What is the intensity of the incident light?

(a) 24.78 W/m^{2} (b) 38.56 W/m^{2} (c) 49.55 W/m^{2}

(a) 0.3 J (b) 1.8 J (c) 18 J (d) 29.7 J (e) 180000 J

A series RLC circuit is driven by a generator with voltage V(t) = 10 sin(100t) volts. At some instant t_{0}, the voltage of the generator was observed to be at its maximum (positive) value. Which one of the following could correctly represent the phasor diagram of this circuit at this instant of time?

(a) (b) (c)

(a) 9.1° (b) 20.2° (c) 49.4° (d) 51.3° (e) 88.0°

(a) P_{average} = 2.72 watts (b) P_{average} = 3.14 watts (c) P_{average} = 5.11 watts (d) P_{average} = 10.5 watts (e) P_{average} = 25.0 watts

What is I_{1} after sending unpolarized light with intensity I_{0} through the same system of polarizers but in the opposite direction (from right to left)?

(a) ¼ I_{0} (b) ½ I_{0} (c) 0

(a) 1.73 nT (b) 2.54 nT (c) 6.47 nT (d) 15.5 nT (e) 35.4 nT

A radio wave (1 MHz) is transmitted around town from a nearby tower. The electromagnetic wave can be represented by the following picture.

What is the wavelength of the signal?

(a) 100 m (b) 150 m (c) 200 m (d) 300 m (e) not enough information

(a) in the +x direction (b) in the +z direction (c) in the -y direction

(a) x direction (b) y direction (c) z direction

(a) 1.0 × 10^{-9} T (b) 2.3 × 10^{-7} T (c) 5.0 × 10^{-6} T

Consider an object 2 cm in height placed 15 cm in front of a concave mirror of focal length f = 5 cm, as shown in this figure.

Which one of the rays in the picture is incorrect?

(a) ray 1 (b) ray 2 (c) ray 3

(a) -2 (b) -0.5 (c) 0 (d) 0.5 (e) 2

(a) Only the top half of the object is imaged. (b) Only the bottom half of the object is imaged. (c) The whole object is imaged, but the image is dimmer.

What is the angle α ?

(a) 17.8° (b) 41.6° (c) 72.2°

An argon-ion laser produces visible light of wavelength λ = 514 nm in air which strikes the top surface of the upper film. The incident light ray is actually vertical. The thickness of the material with index n_{2} is d.

Which minimum value of d can produce a bright reflected beam?

(a) d = 10 nm (b) d = 34 nm (c) d = 69 nm (d) d = 137 nm (e) d = 215 nm