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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.