Physics 106 - How Things Work – Spring, 2001

Problem Set #10 – Optics

The lens of your eye resembles that of a camera—light from the scene in front of you focuses to a real image on your retina. But unlike a camera lens, the lens of your eye can actually change its focal length by changing its curvature. The more curved the lens’s surfaces are, the more strongly it bends light together and the shorter its focal length. The lens’s variable focal length allows you to focus the real image of a particular object onto your retina without having to change the distance between the lens and the retina.

1. Explain why focusing on a distant object requires less lens curvature than focusing on a nearby object.

2. The lens of a farsighted person has trouble becoming curved enough to form a real image of a nearby object on the retina. Explain why eyeglasses containing converging lenses help a farsighted person see nearby objects.

3. The lens of a nearsighted person has trouble becoming flat enough to form a real image of a distant object on the retina. Explain why glasses containing diverging lenses, lenses that bend light rays apart, help a nearsighted person see distant objects.

4. The pupil of your eye changes diameter to control how much light reaches your retina. The brighter the light, the smaller the pupil’s opening. Why is your eye’s depth of focus greater in bright light than in dim light?

A slide projector is essentially the reverse of a camera. Light from an illuminated slide passes through a converging lens and forms a real image on the screen.

5. Since the slide is the object, the object distance is the separation between the slide and the lens. Compare this object distance to the lens’s focal length when the projector casts a real image on a screen far at the other side of a room.

6. You focus the projector by moving the lens toward or away from the slide. If you want to focus the real image on a closer screen, which way should you move the lens?

7. The projector has a zoom lens that changes its focal length when you turn a dial. This lens makes it possible to change the size of the image on the screen. Zooming the lens also moves it toward or away from the slide. As the lens’s focal length increases, should it move toward or away from the slide to keep the real image focused on the screen?

8. Why must the slide be upside down in the projector in order to produce an upright real image on the screen?