Physics 106 - How Things Work - Spring, 2000

Problem Set #9 - Optics

Your eye is very similar to a camera. It has a lens system at the front that bends light to form a real image on its back surface, the retina. The first piece of the lens system at the front of your eye is the cornea, which is curved outward (convex) and transparent. The interface between this surface and the outside air is where most of the refraction necessary to form the image takes place. Behind the cornea is the iris, an aperture that can change the size of its opening, the pupil, to adjust the amount of light entering your eye. Behind the iris is a special lens whose curvature can be changed by the muscles around it, allowing the eye to focus on objects at different distances.

1. Compare the focal length of your eye's lens system when you are focusing on a close object to when you are focusing on a distant object.

2. Describe the size and orientation of the real image formed on your retina when you focus on a near object. Describe the image formed when you focus on a far object.

3. In a near sighted person's eye, the real image from a distant object forms in front of the retina. Modern surgical techniques can correct for this problem by changing the curvature of the front surface of the eye, the cornea. How should the shape of the cornea be changed to correct a near sighted person's vision?

4. In dim lighting your pupils dilate to allow more light to enter your eyes. In bright lighting your pupils contract to limit the amount of light entering your eyes. Why is the image seen by a near sighted person, who is not wearing glasses or contact lenses, sharper under bright lighting?

5. As some people age they develop cataracts, the lenses of their eyes become cloudy obscuring their vision. This can be surgically corrected by removing the cloudy lens and replacing it with a small plastic lens. The shape of the replacement lens is typically chosen so that distant objects will be in focus on the persons retina. Since this lens cannot change shape the person must wear reading glasses to see close objects. How should the reading glasses bend the light rays before they enter the eye?

6. If you open your eyes under water while swimming, everything appears very blurry even if you have perfect vision. Explain why.

Antony van Leeuwenhoek used a very simple microscope to observe microscopic objects with unprecedented resolution in the 17th century. His design was really just a single lens magnifier. The lens was a spherical glass bead, which when held near an object could produce a magnification of 200.

7. Describe the image that you would observe when looking through a glass bead that is very near an object (a distance shorter than the focal length of the bead). Describe the image when the bead is held far away from the object (a distance greater than the focal length).

8. The image observed through the bead will be severely distorted if the whole bead is used to focus the light. To overcome this problem, van Leeuwenhoek placed an aperture in front of the bead so that only the central portion would be used to focus the light. Why is the image distorted when the entire bead is used?