PHYS 252 TEST #2 02/08/08 Dr. Holmes NAME
DO ALL EIGHT PROBLEMS. THE WORTH OF EACH
PROBLEM IS AS MARKED BESIDE THE SPACE FOR THE ANSWER. SHOW YOUR WORK FOR
PARTIAL CREDIT.
1) Laser light of unknown wavelength is
directed through a double slit with a distance of 0.175 mm between slits and
each slit having a width of 0.030 mm. The screen is 7 meters away. The pattern
on the screen has bright spots separated by 2.5 cm.
a) What is the wavelength of the laser
light?
625 nm.
b) What type of light is this (IR, UV,
visible, etc. - if visible, specify the color: blue, green, red, etc.)?
orange
c) If the distance between the slits is
decreased, will the distance between adjacent bright spots increase, decrease,
or remain the same?
Increase
d) If the width of each of the two slits is
decreased, will the distance between adjacent bright spots increase, decrease,
or remain the same?
Remain the same
e) If the wavelength of the light is
decreased, will the distance between adjacent bright spots increase, decrease,
or remain the same?
decrease
2) Laser light of wavelength 632 nm is
directed through a single slit and the pattern is displayed on a screen 7
meters away.
a) If the slit is 0.03 mm wide, how wide is
the full width of the central maximum? (full width is from the dark spot
on one side to the dark spot on the other side of the central bright spot)
29.5 cm
b) If the width of the single slit is
increased, will the full width of the central maximum increase, decrease, or
remain the same?
decrease
c) If the wavelength of the laser is
increased while the slit width is held constant, will the full width of the
central maximum increase, decrease, or remain the same?
increase
3) A sound wave of frequency 15,000 Hz is
incident on a door of width .75 meters. (Assume the speed of sound in air is
340 m/s.)
a) What is the angle for the first minimum
as the sound spreads out behind the door due to the diffraction effects?
1.73 degrees
b) If the frequency were 750 Hz instead,
what would the angle for the first minimum be?
37.2 degrees
4) A Michelson interferometer is to be used
to measure the index of refraction of a certain gas at a certain pressure. A
tube of inside length 6 cm with transparent ends is placed in one
arm of the interferometer. Light of wavelength 632 nm (in vacuum) is
used. Initially the tube has vacuum inside it (no gas). As the gas is slowly
let into the tube, 45 fringes (bright to dark back to bright) are counted.
a) What is the index of refraction of this
gas at the final pressure?
1.00024
b) If green light were used instead, would
there be more, the same, or less fringe shifts for the same experiment?
more
c) If accuracy were extremely important,
which color (green or red) would be better to use to measure the index of
refraction?
green
5) An anti-reflective coating on a lens is
of a material that has an index of refraction of 1.49 and glass has an index of
refraction of 1.87.
a) How thick should the coating be if it is
designed to minimize the reflection of yellow light near normal incidence?
93 nm
b) Will some colors be reflected more than
others? (if yes, which colors will be
reflected more?)
Yes, red and blue
6) In a certain situation, the pupil of a
certain person's eye contracts so that it is 4 mm in diameter.
a) Assuming that the lens and focusing
features of the eye are very good and diffraction is the only limitation on the
ability to see clearly, what is the smallest angle that this person can
resolve? express this angle
in degrees: 0.00961 in arc-minutes: .577 in radians: 0.000174
b) If the light becomes a lot brighter and
the pupil contracts down to 2 mm in diameter to decrease the light
admitted, will the person be able to see small detail more clearly or less
clearly?
Less clearly
7) A camera with a 135 mm focal length lens
takes a picture of an object 50 cm long using an f-stop of 4 and time exposure
of 1/120 sec.
a) If the film is 24 mm x 36 mm in size, and
the image of the 50 cm long object is to fill up the long side of the film (36
mm side), how far away should the object be from the camera?
2.01 m
b) How far should the lens be from the film?
(If the distance is close to the focal length, be sure to indicate whether the
distance is a little more than or a little less than the focal length.)
144.7 mm
c) What is the diameter of the opening to
the lens for this f-stop?
33.75 mm
d) How close can two points of light on the
object be to be resolvable on the film assuming the film itself does not limit
this and lenses are as perfect as possible?
40 m m (4.0 x 10-5m)
e) What is the distance between the image of
the dots of part d above on the film?
2.9 mm
f) If an f-stop of 8 is used, how close can
the two points of light on the object be to be resolvable on the film?
80 m m (8.0 x 10-5 m)
g) What time exposure should be used to
obtain the same amount of light for the film?
1/30 sec
8) Sunlight in June reflects off the calm
(flat) surface of a pond.
a) Can polaroid sunglasses help cut out the reflected glare (answer:
yes or no)?
Yes
b) Will these sunglasses cut out more, the
same, or less glare at 3 pm (assume angle of sun with water is 42 degrees) than
at noon (assume angle of sun with water is 12 degrees) ? (Answer either: more,
same, less, does not apply) ?
More
c) Which polarization should polarized
sunglasses cut out: the horizontal, or the vertical, or doesn't matter, or
both, or neither (i.e., the polaroids are useless in cutting out glare)?
Horizontal.