PURPOSE: To exibit the foci of the Fresnel zone plate corresponding to its focal lengths.

DESCRIPTION: The focal lengths fm of a Fresnel zone plate are given by the relation fm=R1^2/mL, where R1 is the radius of the first zone and L is the wavelength of the light used. A small magnet-mounted diverging lens is placed on the end of the laser, the Fresnel zone plate and a 20 cm focal length convex lens are mounted on a single holder, and a 2 cm focal length convex lens is mounted on a second holder such that it can be moved very close to the first lens. The screen is opposite the laser on a two-meter optical rail.

Start with the moveable lens about 60-65 cm from the screen, and slide it back toward the laser. The first focus you come to (about 68 cm from the screen) corresponds to m=0, the zeroth order of the zone plate. Then, m=1 is at 83 cm, m=3 at 93 cm, m=5 at 97 cm. Between these foci, there is a small, bright "focus" which forms in a manner different from the others. These occur at 89 cm, 96 cm, etc., and correspond to the even orders m=2, 4, 6, etc. Ideally they should not be present beacuse at these distances each transparent annulus contains an even number of Fresnel zones, which should exactly cancel out. That is, the "single slit" diffraction should cancel the interference, just as in the linear diffraction grating. If the rings aren't drawn perfectly, the cancellation isn't perfect, so the even orders are seen, as in the linear grating with slightly different spacing.

Using this technique we find that the measured R1^2/L is 64.1 cm, not 2.3 m as specified on the zone plate. This gives R1=0.64 mm, which is quite accurate.



EQUIPMENT: Laser cart with 2.3 meter focal length Fresnel zone plate, 20cm focal length convex lens, 2cm focal length lens, and screen..

SETUP TIME: 20 min..

Go back to Lecture-Demonstration Home Page.