# Physics 1304/1404 - Spring 1999

# Homework Assignment #7

**Due:** Thursday 15 April 1999

### READING

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.
### ANSWERS

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)**
- the image is inverted for object distances greater than f
- the image is upright for object distances between 0 and f
- the image is real for object distances greater than f
- the image is virtual for object distances between 0 and f
- the image is enlarged for object distances between 0 and 2f
- the image is reduced for object distances greater than 2f

**Q 36-7)**
- the image is never inverted
- the image is always upright
- the image is never real
- the image is always virtual
- the image is never enlarged
- the image is always reduced

**Q 36-11)** M=+1 ; f=infinity

**Q 37-1)**
- the difference in path lengths must be an integer number of wavelengths
(...,-2,-1,0,1,2,...)
- 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 y_{bright}=(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)**
- 4.74 x 10
^{14} Hz
- 422 nm
- 2 x 10
^{8} m/s

**P 35-22)**
- 66.8 microseconds
- 1.0025 times longer

**P 35-24)** 0.395 degrees

**P 35-33)** 63.45 degrees

**P 35-49)**
- 90 degrees (total reflection ALWAYS occurs)
- 30.3 degrees
- 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)**
- -0.204 m
- 0.417 (upright)

**P 36-26)**
- 6.40 cm
- -0.25
- converging

**P 36-33)**
- -12.3 cm
- 0.615
- (diagram required)

**P 36-34)**
- 1 m or 4 m
- 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)**
- 2.62 millimeters
- 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)**
- 6 m
- 3 m

Please report any corrections to
Professor Scalise.

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