PHYS 202 Test #3 3/19/13 Dr. Holmes NAME
DO ALL THE PROBLEMS. THE WORTH OF EACH PROBLEM IS MARKED BESIDE THE SPACE FOR THE ANSWER. SHOW YOUR WORK FOR PARTIAL CREDIT.
1) For the following wavelengths (in vacuum), give the type of light (microwave, x-ray, IR, etc; IF VISIBLE, give the color, i.e., green, red, etc). Also give the frequency for each of the wavelengths:
|
Wavelength |
Type (color) |
Frequency |
|
1.0 x 10-3 m |
Microwave |
3.0 x 1011 Hz |
|
8.0 x 10-5 m |
Infrared |
3.8 x 1012 Hz |
|
6.0 x 10-7 m |
Visible - yellow |
5.0 x 1014 Hz |
|
4.0 x 10-8 m |
Ultraviolet |
7.5 x 1015 Hz |
|
2.0 x 10-10 m |
X-ray |
1.5 x 1018 Hz |
2) a) What is the speed of light in air?
3 x 108 m/s
b) What is the speed of light in glass with an index of refraction = 1.67 ?
1.80 x 108 m/s
c) If light of wavelength 250 nm in glass is used, what is the frequency of this light in glass?
7.2 x 1014 Hz.
On entering the air (from the glass), does the light of part c:
d) change color?
No.
e) change frequency?
No.
f) change wavelength?
Yes, to 418 nm.
3) A light ray coming from air (nair = 1.00) toward glass (nglass=1.67) strikes the air/water surface at an angle of 33° with respect to the SURFACE.
a) What is the angle of REFLECTION as measured from the SURFACE?
33o .
b) What is the angle of REFLECTION as measured from the
57o .
c) What is the angle of the light TRANSMITTED into the water as measured
from the
30.15o .
d) Is it possible for the ray of light in the glass to be totally reflected from the air?
Yes.
e) Would it be possible for a ray of light in the air to be totally reflected from the glass?
No.
4. A person is farsighted and can see things clearly only if they are 67 cm away or farther.
a) What focal length should the person's glasses (lenses) have if they are designed to let the person see something at the near viewing distance of 25 cm clearly?
39.9 cm.
b) Draw a diagram showing the position of the eye, the lens, the object and the image.
c) Is the image provided by the lens upright or inverted?
Upright.
d) Is the lens a converging or diverging lens?
Converging.
e) Draw a diagram of the lens and be sure to indicate positive or negative curvatures for each side of the lens and show clearly whether it is thinner at the edges or in the middle:
5. A lens of focal length 45 mm is used as a magnifying glass.
a) What is the magnifying power of the lens when used correctly?
6.6 X.
b) Draw a diagram showing the lens, its focal length, the eye, the object and the image.
c) Design a lens that has the above focal length of 45 mm, that is, specify nglass, R1 and R2 and draw a picture of the lens:
(many answers - student needs to specify one that works)
FOR PROBLEMS 6 AND 7 USE THE FOLLOWING INFORMATION: A 35 mm camera (film size is 24 mm x 36 mm) uses a lens with a focal length of 120 mm and the f-stop setting is 4 (which means the diameter of the opening to the lens is 1/4 the focal length or 30 mm). You take a picture of a newspaper located 125 meters away. For purposes of calculation assume that the wavelength of the light is one in the middle of the visible spectrum. [If you do not know what wavelength this is, you may ask and I will give it to you but you will be marked down one point.]
6. a) What is the object distance?
125 m.
b) What is the image distance?
120.12 mm .
c) If the print size on the paper is 5.0 mm in height, what is the image height on the film?
4.8 mm = 4.8 x 10-6
m.
d) Is the image upside down or right-side-up?
Upside down.
e) Is the magnification positive or negative?
Negative.
7. a) What is the smallest angle that this camera (f=120 mm) using this f-stop (f/D=2) can resolve based on the Rayleigh criterion?
1.28 x 10-3 degrees = 2.24 x 10-5 radians.
b) What angle does the (5.0 mm) print size make when viewed from 125 meters away?
2.29 x 10-3 degrees = 4.0 x 10-5 radians.
c) Assuming the camera has quality lenses and a fine grain film, can the picture the camera takes be enlarged big enough and clearly enough so that you can read what the newspaper said (definitely, just barely, not quite, definitely not) ?
Not quite.
8) (a) Design a microscope that gives a magnification of exactly 210X, i.e., specify the following:
M = -210
sobj =
L =
s'obj =
fobj =
seye =
feye =
s'eye = -25 cm.
(many possible answers to parameters below - student must correctly
determine these based on the student's choices)
b) Draw a diagram showing the following: position of both lenses, the eye and the object; also indicate on the diagram the distances: L, sobj , s'obj , seye and s'eye .