PHYSICS 132 CHAPTER 36 ANSWERS FOR SOME END OF CHAPTER QUESTIONS
36Q-2
In the lab we combined a diverging lens with a converging lens which converged the light more strongly than the diverging lens diverged the light. Thus the combination of the two lenses still converged the light and acted like a converging lens, and we were able to measure its focal length. Then we could calculate the focal length of the diverging lens using an equation which really came from the thin lens equation. Another way to measure the focal length of a diverging lens would be to place an object a known distance behind the lens and the then observe the image by looking through the lens with a camera or a video camera focused on the virtual image. Then the lens could be removed and a object could be moved back and forth until the position where the object appeared focused when seen through the camera. That way we could find the location of the virtual image. Then we would know both the object distance and the image distance and could use the thin lens equation to calculate f for the diverging lens.
36Q-3
Our eyes have evolved to focus properly in air. Under water there is only a small difference between the index of refraction of the water and the index of refraction of the cornea of the eye, so the cornea does not converge the light properly. In air the curve of the cornea provides about 60% of the converging of the eye. Underwater it is as if your eye is severely far sighted because the light rays do not converge to an image by the time they reach the retina. The use of goggles or a mask puts air next to the cornea again, and allows your eyes to focus properly.
36Q-4
The focal length of a telescope does affect the size of the image of an object. The longer the focal length, the larger the image for an object at a given distance. So a longer focal length telescope will magnify more than a shorter focal length telescope if the same eyepiece is used. If you own a single telescope you change the magnification by using eyepieces of different focal lengths.
36Q-6
A camera is focused by changing the distance between the camera lens and the film. This is the distance q in the thin lens equation. The eye focuses completely differently by changing the focal length of the eye lens, the f in the thin lens equation. The distance between the lens and the image on the retina, the q, remains the same.
36Q-7
When a lens is immersed in water it converges (or diverges, if a diverging lens) the light less rapidly than it does in air because the difference in index of refraction between the lens and the water is less than the difference in index of refraction between the lens and air. So the focal length f is longer in water.
36Q-8
A virtual image cannot be recorded directly on film like a real image can because there are no light rays converging to a focus at the location of a virtual image. However, a virtual image can be seen with your eye and can be photographed with a camera. Another lens is involved in recording a virtual image on film - either a camera lens or your eye lens.
36Q-9
A diverging lens can produce a real image only if combined with a converging lens which converges the light more strongly than the diverging lens diverges the light.
36Q-10
A converging lens cannot form an inverted virtual image by itself. Another lens would have to be involved to produce an inverted virtual image.
36Q-13
for a converging lens:
real if p>f
virtual if p
erect if p
inverted if p>f (a real image)
magnified if p<2f
reduced if p>2f
36Q-14
for a diverging lens:
real never
virtual always, for any p
erect always, for any p
inverted never
magnified never
reduced always, for any p
36Q-15
Yes - see Fig. 36.8
36Q-16
a) If p = 2f, then q = 2f and the image is the same size as the object.
b) With a diverging lens the image is always smaller than the object, except for the trivial case where the object is pressed against the lens.
36Q-18
A converging lens to focus sound waves can be made with a round balloon filled with carbon dioxide gas. Sound travels more slowly through the heavier carbon dioxide molecules than it does through lighter air molecules, so this lens will converge sound. This really works, and makes a fun demonstration. The best way to do it is to have a ticking clock or some other soft sound which you can hardly hear from across the room. You then hold the balloon near your ear (the focal length is very short) and you can easily hear the soft sound. A problem is that a balloon will hold carbon dioxide only for a short time (I have never found out why the carbon dioxide molecules can sneak thorugh the rubber so easily - any chemists out there who can tell me?). We could also make a converging lens by filling a concave balloon (I don't know how to make one) with a gas like helium in which sound travels much faster than it does in air.
36Q-19
If a thin transparent bag filled with air has a convex shape and is placed under water this bag will diverge light and act like a diverging lens, even though the bag is convex. This is because the light will travel much faster in the air inside the bag than in the water around it. So a convex shape converges light only if the the material of the lens slows light down. If light travels faster in the material, a convex shape will diverge light!
36Q-21
The two surfaces of this "lens" have the same curve, and the result is that all incident light rays will be displaced farther from the axis (except the axial ray itself), so this lens will increase the diameter of a beam of light such as the light beam from a laser.