PHYSICS 152

University of Hawaii, Manoa
Dept. of Physics & Astronomy

Instructor: Michael Nassir
Office: Watanabe Hall, Rm. 426, (808) 956-2922
E-mail: nassir @ hawaii.edu

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ANSWERS to Take-Home MIDTERM #3 from FALL 2005

Part A

1a. 4.5x10^4 or 45,000
1b. 6.7x10^9
1c. 14
1d. 5.5x10^3 or 5500
2. (-1 point for each error)
F  (in vacuum, ALL wavelengths travel at the same speed, "c")
F  (yellow has a shorter wavelength than green, hence it has a _lower_ frequency than green: f = c/lambda)
T  
T  (both the E-field and the B-field of EM waves oscillate perpendicularly to the direction of travel)
T  (both the wavelength and the velocity of the light change as the light passes from glass into air, but the frequency does not)
F  (since n_glass > n_air, wavelength in glass < wavelength in air)
T  (Lensmaker's equation shows that f depends on index of lens material and the radii of curvature of both sides of lens)
F  (the height [size] of the mirror is irrelevant; only its radius of curvature matters: f = R / 2)
3. D  (in any medium, v = c/n)
4. D  ("dispersive" means that n [and hence, v] is different for various wavelengths of light)
5a. exactly 50% (or 1/2)
5b. 67 degrees  (Malus's Law: I_2 = I_1 * (cos(theta))^2, and I_2 = 0.15 * I_1 )
6. 53.1 degrees  (Brewster's Angle: tan(theta) = n_2 / n_1 )
7a. 50. cm  (m = -d_i/d_o, where m=-1; then: 1/d_o + 1/d_i = 1/f, solve for d_o and for d_i [for part (b)] )
7b. 50. cm
7c. B  (since d_i is positive)
7d. C  (inverted since m is negative; inverted images are always real [for one-lens systems])

Part B

1a. 61.3 degrees  (Snell's Law: n_plastic * sin(theta_plastic) = n_air * sin(theta_air) )
1b. ray bends upward upon entering air gap (bending away from the normal); ray then bends slightly less upward upon leaving air gap (bending toward the normal)
1c. 13.1 degrees above the horizontal  (use geometry, then use Snell's Law a second time upon leaving air gap)
1d. 53.8 degrees  (sin (theta_critical) = n_air / n_plastic )
1e. the "critical angle"

2a. 589 nm (d = 1 mm/295 lines = 3.39 µm/line; maxima occur at: sin(theta) = m * lambda / d, solve for lambda)
2b. 0.504 nm (same formula as part(a) )

3a. +2.7 times (use Galilean thin-lens equation with d_o=2.5cm and f=4.0cm to find: d_i=-6.67 cm; then use: m=-d_i/d_o to find m)
3b. B  (upright, since magnification is +, and all upright images are virtual [for one-lens systems])
3c. diagram should have 1-cm-tall object at 2.5 cm to the left of the lens, and a 2.7-cm-tall upright image at 6.7 cm to the left of the lens
3d. 4.0 cm  (light from an infinitely distant object [d_o = infinity] forms a focused image at d_i = f = 4.0 cm; OR: light from an infinitely distant object arrives in parallel rays, and a converging lens focuses incoming parallel rays at distance "f" on the opposite side of the lens)

4a. 45 degrees
4b. 1.85
By inspection of the geometry, the light ray is incident at 45 degrees to the normal of the glass.
Also, the triangle formed by the ray and two radii inside the cylinder is an isoceles triangle whose internal angles must add to 180 degrees; therefore, the angle of the light ray to the normal inside the glass at BOTH surfaces is 22.5 degrees. Using Snell's Law at both interfaces, we find both that n = 1.847 and that the final refracted angle is 45 degrees.