# Homework Assignment #7

Due: Thursday 15 April 1999

Chapters 35, 36, and 37.

### QUESTIONS

Chapter 35 - 1, 3, 4, 6, 8, 18.
Chapter 36 - 2, 3, 4, 6, 7, 11.
Chapter 37 - 1, 2, 3.

### PROBLEMS

Chapter 35 - 8, 9, 22, 24, 33, 49.
Chapter 36 - 3, 5, 10, 26, 33, 34.
Chapter 37 - 1, 9, 17A, 17, 34, 38, 40, 49.

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 35-1) The ray approximation is valid if lambda << d, that is, if the wavelength of the incoming light is much smaller than the slit width.

Q 35-3) No. Light traveling from a medium with a small index of refraction to a medium with a large index of refraction (e.g. air to water) is bent toward the normal. However, light traveling from a medium with a large index of refraction to a medium with a small index of refraction (e.g. water to air) is bent away from the normal.
Q 35-4) The wavelength and speed change; the frequency does not change.
Q 35-6) Since the refracted ray is bent toward the normal, the index of refraction of Lucite must be larger than the index of refraction of air.
Q 35-8) The difference between the indices of refraction of two media makes the interface visible. The index of refraction of liquid helium is very close to that of air.
Q 35-18) If X is bent more than Y, then the index of refraction for X must be larger than the index of refraction for Y, n(X)>n(Y). Since the speed of light in a medium is v=c/n, color X travels more slowly, v(X)<v(Y).
Q 36-2) A flat mirror need only be half as long as you are tall.
Q 36-3) The image is not always inverted. The image is not always real.

For object distances between 0 and f, the image is virtual and upright.
For object distances greater than f, the image is real and inverted.

For object distances between 0 and 2f, the image is enlarged.
For object distances greater than 2f, the image is reduced.
Q 36-4) The image is always virtual, upright, and reduced.
Q 36-6)
1. the image is inverted for object distances greater than f
2. the image is upright for object distances between 0 and f
3. the image is real for object distances greater than f
4. the image is virtual for object distances between 0 and f
5. the image is enlarged for object distances between 0 and 2f
6. the image is reduced for object distances greater than 2f

Q 36-7)
1. the image is never inverted
2. the image is always upright
3. the image is never real
4. the image is always virtual
5. the image is never enlarged
6. the image is always reduced

Q 36-11) M=+1 ; f=infinity
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).
P 35-8) 75 cm
P 35-9)
1. 4.74 x 1014 Hz
2. 422 nm
3. 2 x 108 m/s

P 35-22)
1. 66.8 microseconds
2. 1.0025 times longer

P 35-24) 0.395 degrees
P 35-33) 63.45 degrees
P 35-49)
1. 90 degrees (total reflection ALWAYS occurs)
2. 30.3 degrees
3. total internal reflection NEVER occurs because the beam is traveling from a lower index of refraction to a higher one.

P 36-3) 2'11"
P 36-5) 30 cm
P 36-10)
1. -0.204 m
2. 0.417 (upright)

P 36-26)
1. 6.40 cm
2. -0.25
3. converging

P 36-33)
1. -12.3 cm
2. 0.615
3. (diagram required)

P 36-34)
1. 1 m or 4 m
2. Both images are real and inverted, but the magnifications differ.
When the lens is 1 m from the object, the magnification is -4.
When the lens is 4 m from the object, the magnification is -0.25.
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

Please report any corrections to Professor Scalise.