PHYS 202 Test #3 3/14/08 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 |
|
2.5 m |
FM radio |
1.20 x 108 Hz = 120 MHz |
|
3.6 x 10-3 m |
Microwave |
8.33 x 1010 Hz = 83 GHz |
|
8.9 x 10-5 m |
Infrared |
3.37 x 1012 Hz |
|
5.4 x 10-7 m |
green |
5.56 x 1014 Hz |
|
7.4 x 10-19 m |
Ultraviolet |
4.05 x 1016 Hz |
2) a) What is the speed of light in air?
3 x 108 m/s
b) What is the speed of light in water (index of refraction of water = 1.33) ?
2.26 x 108 m/s
c) If light of wavelength 632 nm (in air) is used, what is the frequency of this light in air?
4.75 x 1014 Hz.
On entering the glass (from the air), does the light:
d) change color?
No.
e) change frequency?
No.
f) change wavelength?
Yes, to 475 nm.
3) A light ray coming from air (nair=1.00) toward water (nwater = 1.33) surface strikes the air/glass surface at an angle of 65° with respect to the SURFACE.
a) What is the angle of REFLECTION as measured from the SURFACE?
65o .
b) What is the angle of REFLECTION as measured from the NORMAL?
25o .
c) What is the angle of the light TRANSMITTED into the glass as measured from the NORMAL? (if totally reflected, write TIR)
18.5o .
d) Would it be possible for a ray of light in the air to be totally reflected from the water?
No.
e) Is it possible for the ray of light in the water to be totally reflected from the air?
Yes.
4. A person is nearsighted and can see things clearly only if they are 70 cm away or closer.
a) What focal length should the person's glasses (lenses) have if they are designed to let the person see something at the far viewing distance of 100 m clearly?
-70.5 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?
Diverging.
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 4.0 cm is used as a magnifying glass.
a) What is the magnifying power of the lens when used correctly?
7.25 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 4.0 cm, 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 80 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?
80 m.
b) What is the image distance?
120.18 mm .
c) If the print size on the paper is 4.0 mm in height, what is the image height on the film?
-6.0 mm.
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=4) can resolve based on the Rayleigh criterion?
1.28 x 10-3 degrees = 2.24 x 10-5 radians.
b) What angle does the (4.0 mm) print size make when viewed from 80 meters away?
2.86 x 10-3 degrees = 5.0 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 / Just barely.
8) (a) Design a microscope that gives a magnification of exactly 420X, i.e., specify the following:
M = -600
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 .