Diffraction

In this lab the phenomenon of diffraction will be explored. Diffraction is interference of a wave
with itself. According to Huygen’s Principle waves propagate such that each point reached by a
wavefront acts as a new wave source. The sum of the secondary waves emitted from all points on
the wavefront propagate the wave forward. Interference between secondary waves emitted from
different parts of the wave front can cause waves to bend around corners and cause intensity
fluctuations much like interference patterns from separate sources. Some of these effects were
touched in the previous lab on interference.
In this lab the intensity patterns generated by monochromatic (laser) light passing through a single
thin slit, a circular aperture, and around a opaque circle will be calculated and experimentally
verified.

The intensity distributions of monochromatic light diffracted from the described objects are based
on:
a) the Superposition Principle
b) the wave nature of light
Disturbance: A = A0 sin (wt + €)     w for Omega, € for teta (angle on degrees)
Intensity: I = (EA)2    E for Sigma
c) Huygen’s Principle -- Light propagates in such a way that each point reached by
the wave acts as a point source of a new light wave. The superposition of all these
waves represents the propagation of the light wave.
All calculations are based on the assumption that the distance L between the slit and the viewing
screen is much larger than the slit width a:, i.e. L >> a. This particular case is called Fraunhofer
scattering. The calculations of this type of scattering are much simpler than the Fresnel scattering
in which case the L >> a constraint is removed.

Experiment 1 : Single Slit Diffraction
Theory

A narrow slit of infinite length and width a is illuminated by a plane wave (laser beam) as as shown in Figure 1. The intensity distribution observed (on a screen) at an angle q with respect to the incident direction is given by equation (1). This relation is derived in detail in the appendix and every student must make an effort to go through its derivation. The mathematics used to calculate this relation are very simple. The contributions from the field at each small area of the slit to the field at a point on the screen are added together by integration. Squaring this result and disregarding sinusoidal fluctuations in time gives the intensity. The main difficulty in the calculation is determining the relative phase of each small contribution. Figure 2 shows the expected shape of this distribution. 

Diffraction Single slit

yielding the following condition for observing a minimum light intensity from a single slit:

This relation is satisfied for integer values of m. Increasing values of m give minima at correspondingly larger angles. The first minimum will be found for m = 1, the second for m = 2 and so forth. If 
is less than one for all values of q, there will be no minima, i.e. when the size of the aperture is smaller than a wavelength (a < l). This indicates that diffraction is most strongly caused be perturbances with sizes that are about the same dimension of a wavelength.

 

Procedure
Two single slits (along with some double slits) are on a slide similar to the one diagrammed in Figure 3. To observe diffraction from a single slit, align the laser beam parallel to the table, at the height of the center of the long slide, as shown in Figure 4. The diffraction pattern you are expected to observe is shown in Figure 5.

1a) Observe on the screen the different patterns generated by both of the single slits of this slide.
1b) Calculate the width of each one of the two single slits. This quantity can be calculated fro

Equation (2) using measurements of the spacing of the intensity minima. The wavelength of the
HeNe laser is 6328Å, (1Å º 10-10 m). The quantity to be determined experimentally is sin q. This
can be done by trigonometry as shown below:

Measure the slit width using several intensity minima of the diffraction pattern.This measurement can be done using the screen covered with white paper. With a sharp pencil mark the position of the diffraction minima and then measure their relative distance with the ruler. To improve the accuracy of your measurements make the distance from slit to screen as large as possible. Compare your result with those given in Figure 1.
Enough for this time, next...Experiment 2 : Diffraction by circular aperture