# Homework Assignment #8

Due: Tuesday 28 July 1998

Chapters 37 and 38.

### QUESTIONS

Chapter 37 - 1, 2, 3.
Chapter 38 - 1, 3, 8, 11.

### PROBLEMS

Chapter 37 - 1, 9, 17A, 17, 34, 38, 40, 49.
Chapter 38 - 1, 4, 29, 36, 50, 54.

These are the ANSWERS only, not the SOLUTIONS. It is not sufficient to copy these and turn them in as homework. You must show your work.

Q 37-1)

1. the difference in path lengths must be an integer number of wavelengths (...,-2,-1,0,1,2,...)
2. the difference in path lengths must be an odd half-integer number of wavelengths (...-5/2, -3/2, -1/2, 1/2, 3/2, 5/2...)

Q 37-2) The two sources are incoherent -- they do not maintain a constant phase with respect to each other.
Q 37-3) The wavelength of light shrinks by a factor of n (the index refraction) in water. In Young's double slit experiment, the positions of the bright fringes are given by ybright=(lambda)Lm/d (Equation 37.5). L is the distance from the slits to the screen; that remains the same. d is the slit separartion; that remains the same. If the wavelength shrinks in water, then the bright fringes in the interference pattern must move closer together (so do the dark bands).
Q 38-1) The Fraunhofer pattern occurs when the rays are nearly parallel, either because the screen is far from the slit, or because a lens was used to make the ligth rays parallel.

The Fresnel pattern occurs close to the screen and is much more complicated to describe mathematically.

Q 38-3) The width of the central maximum gets larger. Look at Figure 38.7. The central maximum extends from sin(theta)=+lambda/a to sin(theta)=-lambda/a. As the slit width "a" is made smaller, the angles "theta" become larger.
Q 38-8) In early morning or late evening, when the Sun is close to the horizon, the light coming from the zenith is highly polarized. You can check this with a polarizing filter.

Light scattering many times in clouds (that's why they are white) loses its polarization. When you look at a cloud against the blue sky through Polaroid glasses, the polarized light of the sky is blocked but the unpolarized light from the cloud gets through.

Q 38-11) The obsidian glass is too dark for one to see the refracted ray inside the sample, but one can use Brewster's angle to measure n. Shine an incident beam of unpolarized light on a flat sample of obsidian. Vary the angle of incidence until the reflected beam is most polarized. This is Brewster's angle, and the index of refraction n=tan(Brewster's angle).
P 37-1)
1. 2.62 millimeters
2. 2.62 millimeters (same as above)

P 37-9) 1.25 m
P 37-17A) lambda/2(n-1)
P 37-17) 343 nanometers
P 37-34) 658 nanometers
P 37-38) 290 nanometers
P 37-40) 5 millimeters
P 37-49)
1. 6 m
2. 3 m

P 38-1) 632.8 nanometers (the wavelength of the light)
P 38-4) 4.22 millimeters
P 38-29) 0.068 degrees
P 38-36) 3646
P 38-50) 36.87 degrees above the horizon
P 38-54)
1. 6.88 units
2. 5.63 units

Please report any corrections to Professor Scalise.