PHO 101 Photonics Concepts
Three Rivers Community College ONLINE

Home Lab #9

Rayleigh's Criterion

Objectives

Equipment/Supplies

 

Theoretical overview

The diffraction pattern formed at a distance from a circular opening consists of a central disk ("Airy disk") surrounded by lower intensity concentric fringes. If light of wavelength l passes through a circular opening of diameter D, the angular half width of the diffraction disk is given by

Consider two closely spaced point sources of light, a distance x apart and a distance y from a lens of diameter D. Each source will produce its own diffraction disk with a size determined by the equation above. Rayleigh's criterion states that the two points will be just resolved when the center of one diffraction disk falls on the edge of the other.

Rayleigh's criterion for this situation is

The distance (x) at which two closely spaced objects are resolved depends on the wavelength (l) and on the diameter of the opening through which the light passes. This could be the rim of a lens or the pupil of an eye. In the case of an eye, a row of closely spaced dots will appear as a solid line if the diffraction disks overlap on the retina.

Procedure

1. Stand far enough away from the red and blue patterns so that they appear to be solid lines. Walk slowly toward the patterns until each resolves into a set of dots. Record the distance at which the dots are resolved for both the red and blue patterns.

2. Repeat the experiment with the room lights dimmed. (The pattern should be illuminated.)

Questions/Conclusions

1. Does the distance at which the spots can be resolved depend on wavelength? (color) If so, how?

2. Based on Rayleigh's criterion, in what order should the spots have been resolved as the person walked toward the test paper?

3. Why should the resolution (the distance at which either color dots are resolved) depend on whether or not the room lights are on?

Applications/Explorations

Even though an eye doctor may have told you that you have "perfect vision", the resolution of your eyes is limited by diffraction and Rayleigh's criterion. This limits how small letters can be on signs, and how close together lights on an airport tower can be. It also explains the style of painting called Pointillism, or stippling. In these paintings, millions of tiny dots that merge together when viewed from a distance. In such paintings, two neighboring dots of different color can appear to form a third color when viewed from far away. How can this be?

If you live near an art museum, see if they have any Pointillistic paintings on display and note at what distance the different color dots begin to merge.