Question

Learning Goal: To use the formulas for the locations of the dark bands and understand Rayleigh's criterion of resolvability.

An important diffraction pattern in many situations is diffraction from a circular aperture. A circular aperture is relatively easy to make: all that you needis a pin and something opaque to poke the pin through. The figure shows a typical pattern. It consists of a bright central disk, called the Airy disk,surrounded by concentric rings of dark and light.

While the mathematics required to derive the equations for circular-aperture diffraction is quite complex, the derived equations are relatively easy to use.One set of equations gives the angular radii of the dark rings, while the other gives the angular radii of the light rings. The equations are the following:

,

,

where is the wavelength of light striking theaperture, is the diameter of the aperture, and is the angle between a line normal to the screen and a linefrom the center of the aperture to the point of observation. There are more alternating rings farther from the center, but they are so faint that they are notgenerally of practical interest.

Consider light from a helium-neon laser (nanometers) striking a pinhole with a diameter of 0.425 .

a. At what angle $theta_1$ to the normal would thefirst dark ring be observed?

b. What is the angular radius $theta_1$ of the firstdark ring for a point source being imaged by this telescope? Use nanometers for the wavelength, since this is near the average for visible light.

Answer 1