Optical Diffraction

This experiment examines certain consequences of the wave nature of light. Various objects will be placed in the path of a plane wave of light generated by a He-Ne laser and beam expanding optics, and the resulting patterns will be measured quantitatively using a photocell detector and compared with theoretical predictions.
 

Background:

1. What assumptions are the basis of Fresnel diffraction, and what limiting case Fraunhofer diffraction is of the more general Fresnel diffraction.
2. The derivation of the Fraunhofer diffraction pattern for a single slit, two slits, and then N slits.

The relation of Fraunhofer diffraction to the Fourier (integral) transform.
3. Qualitative description of diffraction in the Fresnel approximation.

Bibliography:

• Smith and Thomson, Optics (1971). *
• Moller, Optics, (1988). *
• Jenkins and White, Fundamentals of Optics, 4th ed. (1976)
• Mathieu, Optics (1975)
• Stone, Radiation and Optics (1963)
• Klein and Furtak, Optics (1986)

Apparatus:

1. He-Ne laser with "spatial filter", which consists of a short focal length lens and a pinhole at the focal point. This eliminates off-axis or scattered light from the laser, and produces a smooth coherent beam diverging from an effective point source.
2. Optical bench, with mounts for several lenses, etc.
3. Photodiode/op amp behind a slit, mounted on a translation stage, and X-Y recorder.
4. Various diffracting objects:
• Single Slits (fixed and variable width)
• Double slits
• N Slits (N = 3, 4, many)
• Circular aperture, or array of apertures
• Knife Edge
5. Microscopes (travelling, or with graticule) for measuring object dimensions.

Setup Notes on Fraunhofer Diffraction

This configuration is usually the most convenient, especially for the ultrasonic experiment, but Fraunhofer diffraction is obtained under more general conditions, namely at any plane where the laser is brought to a focus in the absence of the diffracting screen. (To understand this, start from the variational principle according to which the optical path length from the spatial filter to the focal point is the same for any geometric ray through the optics.) This can be done with a single lens suitably placed either in front or in back of the diffracting screen. In this case the scale of the diffraction pattern must be calibrated.
 

Measurements:

1. Set up the apparatus for Fraunhofer diffraction and test with the single slit diffraction pattern.Vary slit width, record some patterns (and measure the corresponding slit width), and explain differences in the observed diffraction pattern.
2. Record the double slit pattern. Explain both the peak positions and the envelope in terms of Fourier optics or the classical N-slit diffraction formula. Do the same for N = 3, 4.
3. Visually observe the diffraction pattern from a circular aperture and compare your results with theory. Observe and sketch the pattern from an array of apertures, and interprete, specifically, what is due to the size and chape of an individual aperture and what is due to interference between apertures.
4. Record the Fresnel diffraction pattern exhibited by a knife edge. Compare with theory. (No lenses are needed after the spatial filter. There is one length parameter in the problem: The distance from the knife edge to the pinhole.) Also examine Fresnel diffraction by a wire (say, a paper clip).

Diffraction by Ultrasonic wave:

1. Replace the diffracting screen by the water trough.
2. See separate instruction sheet [unwritten].