The following test consists of 10 Multiple Choice questions and 5 problems worth a total of 100 points. There is no partial credit on the multiple choice—choose the letter of the best answer. However, your reasoning must be shown to receive full credit on the problems. Your job is to convince me not only that you can get the correct answer, but also that you can explain to someone else how you got to that answer.
Part I: Multiple Choice
1. A goldfish is sitting at the bottom of a calm pond. You note that you cannot see the fish from above the water’s surface once you are off to the side by a certain amount. This is most likely due to
a. the refraction of the light reflecting off of the goldfish.
b. the law of reflection. c. Rayleigh’s criterion. d. Brewster’s angle.
e. the onset of total internal reflection.
2. If the image distance for a thin lens is positive but the magnification is negative, then the image is
a. real and inverted b. real and upright c. virtual and inverted
d. virtual and upright e. It depends on the focal length–not enough information is given.
3. Most of the focusing of the eye occurs at the
a. cornea b. aqueous humor c. eye lens d. ciliary e. retina
4. A material is said to be optically active if
a. it glows when light is incident on it. b. it melts when light is incident on it.
c. it rotates the polarization vector of the light as it travels through the material.
d. it gradually eliminates the polarization of the light as it travels through the material.
e. it turns the light into two polarization directions as it is refracted through it.
5. You are watching an approaching distant light. At some known distance from you, you realize that it is really a pair of lights approaching you. At this distance, the separation between the two lights can be determined from
a. the critical angle. b. Brewster’s angle. c. the Rayleigh angle.
d. Snell’s law. e. the angle of incidence.
6. Light of wavelength 570 nm in air enters glass of index of refraction 1.53. What is the wavelength of the EM radiation after it enters the glass?
a. 152 nm b. 373 nm c. 570 nm d. 872 nm e. 935 nm
7. Blue light has a wavelength closest to
a. 410 nm b. 470 nm c. 580 nm d. 620 nm e. 670 nm
The remaining multiple-choice questions refer to the following set-up.
You carefully drill a number of small holes of known diameters in a sheet of dark plastic. You then set up a diffraction experiment in which you shine laser light through each hole and measure the radius of the resulting Airy disk on a screen which is 1.7 m distant. You record the data for the radii of the Airy disks, r1, and the diameters of the holes, d. You determine that the largest fractional uncertainty has the value 0.2 and comes from the hole-diameter data.
8. What plot of your data should you make to get a linear plot?
a. d vs. r1 b. d2 vs. r1 c. r12 vs. d d. r1 vs. 1/d e. r1 vs. 1/d2
9. When you plot the graph mentioned above, you get a slope (in MKS units) of 1.08 x 10–6. What is the wavelength of the laser light being used?
a. 420 nm b. 470 nm c. 520 nm d. 580 nm e. 630 nm
10. What is the uncertainty (in MKS units) in the value of the slope given above?
a. 0.1 x 10–6 b. 0.2 x 10–6 c. 0.5 x 10–6 d. 0.8 x 10–6 e. 0.9 x 10–6
Part II: Problems
1. You are standing on a dock looking down at a small, shiny metal box on the bottom of a clear pond. The light rays reaching your eyes from the box make an angle of 55o from the horizontal. The depth of the pond is H = 2.4 m in the region of the box. The index of refraction of the pond water is 1.3.
(a) What is the angle of transmission, qt, for the box’s rays reaching your eyes from the water’s surface?
(b) What is the angle of incidence, qi?
(c) What is the speed of light as it travels through the pond water?
(d) Light reaching your eye from the box appears to be red. What is the approximate wavelength of this light in air?
(e) What is the frequency of the light in part (d)?
(f) What was the wavelength of the light in part (d) when it was in the water?
2. (a) A 2.0-cm tall object is standing 20.0 cm in front of a 10.0 cm focal length converging lens. Find and describe the image of the object in the lens analytically.
(b) Verify your answers above in part (a) by solving the problem graphically (showing all 3 rays) on the figure below. (Each tick-mark designates 10.0 cm.) Be sure to draw in the final image.
(c) A 2.0-cm tall object is standing 20.0 cm in front of a 10.0 cm focal length diverging lens. Find and describe the image of the object in the lens analytically.
(d) Verify your answers in part (c) above by solving the problem graphically (showing all 3 rays) on the figure below. (Each tick-mark designates 10.0 cm.) Be sure to draw in the final image.
3. A friend of yours cannot see objects clearly that are further away than about 60 cm.
(a) Is your friend myopic or hyperopic? Explain this vision defect with as much detail as you can.
(b) Find the prescription of your friend’s eyeglasses in diopters.
(c) Your friend’s optician has a “lens blank” having an index of refraction 1.60 which can be ground to different radii on its two sides to form a lens of a specified prescription. Determine a possible set of two radii of curvature for your friend’s eyeglass lenses that would result in the proper prescription for your friend. (You can just make a reasonable guess for one of the radii, and then compute the other.) Also make a rough sketch of the lens showing the two radii of curvature (as was done in class).
4. Unpolarized light of intensity Io = 45 W/m2 is incident on a set of two ideal Polaroids. What is the smallest angle between the transmission axes of the two Polaroids if the intensity of light emerging from the second Polaroid is I2 = 15 W/m2 ?
5. Laser light of wavelength 670 nm is incident on a small circular aperture. The light emerging from the aperture is then incident on a viewing screen which is 85 cm from the aperture.