Physics 102

Chapter 28, Homework Solutions

Exercises:

2) You see card 2. The light must bounce off the mirror so that the angle of reflection = the angle of incidence.

4) For a trucker to see you, light (from somewhere) must be reflected from you, reflected from one of the truck's mirrors, and hit the trucker's eye. If you cannot see the mirror, then light from you cannot hit the mirror. If light from you cannot hit the mirror, then the trucker cannot see you. This is summarized in the technical theorem: `I see you, you see me'.

10) It is easier to see a pebbled road surface at night. This is because your light source at night are your headlights. For you to see the road, light must be emitted from the headlights, hit the road, and be reflected back to you. A mirror smooth road will reflect the light forward, ie: away from you (so angle of incidence = angle of reflection). A pebbled road surface will reflect light in all directions (like a movie screen) and some will be reflected back to you.

16) The window is half the height of each twin and goes from the height of the top of their heads to half-way down. Eg: if each twin is 6' tall, then the window extends from 6' to 3' high.

28) Light going from the water to the air refracts so that it bends away from the normal. A light ray at 48 degrees from the normal in the water will be refracted so it is at 90 degrees from the normal in the air (ie: so it is parallel to the water surface). Light at greater than 48 degrees would refract at an angle greater than 90 degrees and end up back in the water. Thus it cannot happen. Light going from the air to the water refracts so that it bends towards the normal. Even light hitting the water at an angle of almost 90 degrees can refract (and would end up at 48 degrees from the normal in the water).

Another way to answer this is to look at figure 28.36. You can see that the maximum angle for light transmitted from water to air is 48 degrees. Now reverse all the light rays. You can see that there is no maximum angle. Light from the air can be at any angle from 0 to 90 degrees and still enter the water.

30) The weight of the water strider pushes down on the water surface and makes dimples on it (one at the end of each leg). This dimple functions as a diverging lens (see figure 28.44b). When the rays of light hit the water surface, they refract a bit, hit the bottom and are reflected from the bottom. We see the bottom using this light reflected from the bottom. When the rays of light hit the dimple, they spread out (see figure 28.44b). This means that none of the light hits the bottom below the dimple. This makes the dark spot. The light rays are all refracted outward by the lens so they make a bright ring around the dark spot.

Note that the shadow under the body of the insect is different. The shadow is caused by light being absorbed by the insect's body and not reaching the bottom of the water. There are no bright rings around this shadow. On the other hand, the shadow under the insect's feet is caused by light being redirected. That means that the total light hitting the bottom is unchanged, it is redirected so that there are dark spots and compensating bright rings.

36) No. A transparent pool cover lets all the sunlight that hits it go through and be absorbed by the pool. The `solar heat-shields' do the same thing. No extra light is collected by the `solar heat-shield'. At most, the lenses might redirect the light that hits it to different points in the pool. This means that they would leave bright spots and compensating dark spots (see exercise 30).

Two minor points: 1) air filled lenses will not have much focusing power. 2) Air filled spaces are very good thermal insulators, so the `solar heat-shield' probably will keep the pool warmer by letting less heat escape than would a thin plastic sheet.

42) This is the same question we asked in class with the image projected onto the screen by a lens. When we covered half the lens in class, the image got a little darker (since only half the light got through) but the whole image was still there. Covering the top half of a camera lens will just make the picture a little darker.

44) A simple magnifying glass under water will magnify less. A magnifying glass works by refracting the light rays that hit it. When it is in air, the index of refraction of the glass is about 1.5 and the index of air is about 1. This is a big difference in speed of the light rays so they refract a lot. When you put the magnifying glass in water, the indices of refraction are just 1.5 (glass) and 1.33 (water) so the there is a much smaller difference in the speed of the light rays. Thus, the light will refract less and there will be less magnification.

This is just like the film we saw in class where the eye-dropper disappeared when the index of refraction in the eye-dropper and the liquid matched.

It is also like the fact that near-sighted people can see more clearly underwater (without goggles).

Problems:

2) The image of the butterfly appears to be 20 cm behind the mirror. Thus, it is 20 cm + 50 cm = 70 cm from your eye.

4) You walk toward the mirror at 2 m/s. Your image appears to walk toward the mirror (from the other side) at 2 m/s. Thus, you approach your image at 4 m/s.

Estimation:

a) If 40,000 Americans are killed on the roads each year, then that is about 100 per day. Therefore it takes 1/2 day or 12 hours for cars and trucks to kill 50 Americans.

b) Tobacco kills 400,000 Americans per year. That is about 1000 per day. Therefore it takes (50/1000) days = 1/20 day = about 1 hour for tobacco to kill 50 Americans.

Please note that I am not trying to minimize the impact of these deaths. Almost all deaths are tragedies. The point here is that there is a societal cost to whatever we do. As a society, we choose to drive, knowing that this will kill many people each year. As a society, we choose to allow smoking, knowing that this will kill many people each year. As a society, we chose to invade Iraq, knowing that this will kill people. The question to ask is whether the benefits outweigh the costs.