Supplementary Problems for Physics 241
Final Examination
1. James Bond is swimming 3.00 m underwater with a flashlight. A guard is standing on an enemy boat 6.00 m in front of him. If Bond shines the flashlight at a point on the water that is 2.00 m in front of the boat, is it possible for the guard to see the beam?
2. Someone observing a fish tank from above sees a goldfish 2.00 cm beneath the surface. What is the actual distance of the goldfish from the surface?
3. A radio station is authorized to broadcast at 100,000 watts.
a. What is the amplitude of the electric field of the station’s broadcast at a distance of 1.00 km from the station’s transmitter? (Treat the transmitter as a point source.)
b. Assuming a radio antenna 1.00 km from the transmitter completely absorbs the signal, what is the radiation pressure of the signal on the antenna?
4. Sherlock Holmes is using his magnifying glass to observe a mark on a wall. If the magnifying glass is held 4.0 cm from the wall and it makes the mark appear three times as large as it really is, what is the focal length of the magnifying glass?
5. An object 2.00 cm tall is placed 6.00 cm in front of a concave mirror of radius 10.0 cm.
a. Find the image distance. Is the image real or virtual?
b. How tall is the image? Is the image upright or inverted?
c. Make a ray diagram showing how the mirror forms the image.
d. Repeat this problem for the case of a convex mirror.
6. An object 1.00 cm tall is placed 3.00 cm in front of a converging lens with focal length 2.00 cm.
a. Find the image distance. Is the image real or virtual?
b. How tall is the image? Is the image upright or inverted?
c. Make a ray diagram showing how the lens forms the image.
d. Repeat this problem for the case of a diverging lens.
7. Unpolarized light of intensity I is incident on a crossed polarizer-analyzer pair.
a. What is the intensity of the light emerging from the analyzer?
b. Suppose a third polarizer is placed between the polarizer-analyzer pair so that its polarization direction makes an angle of 30° with respect to the first polarizer. What is the intensity of the light emitted from the analyzer?
Answers to Supplementary Problems for Physics 241
Final Examination
1. First find the angle of incidence of the flashlight’s beam with the water. (See the figure at the right.)
Since the angle of incidence of the beam exceeds the critical angle, the beam undergoes total internal reflection back into the water. Hence the guard cannot see the beam.
Remark. Note that the above is an idealized situation.It is assumed that the beam from the flashlight is collimated, that is, all the rays in the beam are parallel. This is not true for ordinary flashlights, so it might be possible for some of the rays of the beam to be seen above water. In the above example we can assume that Mr. Bond is using one of his fancy gadgets: a highly-collimated waterproof laser flashlight.
2. Because of refraction objects submerged in a liquid (such as water) are actually deeper than they appear.
Consider the figure at the right. A goldfish submerged at depth d in water reflects a light ray to the surface. (For simplicity the ray reflected at the surface is omitted.) Someone observing the fish from above the surface, however, sees the fish at depth d¢, which is smaller than d.
We see that Thus
This formula is generally true. However, if the angles of incidence and refraction of the light ray are small we may use the approximation so that
Solve the above equation for d:
Keep in mind that this is an approximation valid for small angles. If the angles are large, it gives just a rough estimate of the actual depth.
3. a. E = 2.45 V/m b. pr = 26.5 pPa
4. f = 6.0 cm
5. a. q = +30.0 cm; image is real. b. hi = -10.0 cm; image is inverted. c. You do. d. You do.
6. a. q = +6.00 cm; image is real. b. hi = -2.00 cm; image is inverted. c. You do. d. You do.
7. a. 0 b.