PINHOLE DIFFRACTION

Experiment 112-6
Diffraction and Interference
Introduction
Figure 6.1 Single Slit Diffraction Pattern
Single Slit Diffraction: When light passes through a narrow slit, a diffraction pattern consisting of a series of dark and light bands, or fringes, is observed. As you can see in Figure 6.1, the pattern is most intense at the central maximum. The condition for the nth minimum of intensity due to diffraction is given by the equation
sinnw??sinnw??=, (6.1)
where is the angular displacement of the minimum from the location of the central maximum, w is the width of the slit, and ? is the wavelength of the incident light. The integer n denotes the order of the minimum; that is, ?n1= denotes the first order, 2n= the second order, and so on. Note also that the bright fringes, or maxima, occur midway between the minima. Their intensity is considerably less than that of the central maximum.
Figure 6.2 Double Slit Diffraction &
Interference Pattern
Double Slit Diffraction and Interference: When light passes through two narrow slits separated by a distance d, a combined diffraction and interference pattern like the one illustrated in Figure 6.2 is usually observed. The locations of the more widely separated diffraction minima are determined by the width of the slits, and are given by equation (6.1). The condition for the mth maximum due to interference is given by the equation
sinmd??=, (6.2)
where ? is the angular displacement of the maximum from the location of the central maximum, d is the center-to-center separation of the slits, and m is the order of the maximum. Dark fringes, or minima, occur midway between the maxima.
Combined diffraction and interference patterns like the one illustrated in Figure 6.2 are only observable for reasonable combinations of slit width and slit separation. If the slits are too narrow the diffraction minima will be so widely separated as to be unobservable. On the other hand, if the slit separation is too wide, the interference maxima will be so closely packed as to be indistinguishable.
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Diffraction & Interference Experiment 112-6
Circular Diffraction: When light passes through a circular aperture, a diffraction pattern like the one illustrated in Figure 6.3 is observed. The location of a maximum or a minimum of intensity is given by
sinka? ? =, (6.3)
where a is the diameter of the aperture and the value of k depends upon which dark or light ring is observed. Values of k for the first five dark and the first five bright rings are given in the table below. As an example, the criterion for the formation of the third dark ring is given by 3.24sina??=.
Ring
number
k
(dark rings)
k
(bright rings)
1
1.22
1.64
2
2.23
2.69
3
3.24
3.72
4
4.24
4.72
5
5.24
5.72
Figure 6.3 Circular Diffraction
Purpose
The purpose of the experiment is to use diffraction and interference patterns to determine (1) the width of a single slit, (2a) the width of the individual slits making up a double slit, (2b) the distance between the two slits, and (3) the diameter of a circular pinhole.
IMPORTANT SAFETY NOTES!
Although the lasers used in this laboratory are of low power, they still produce a very intense beam and must be treated with respect. The beam is not of sufficient intensity to cause skin burns but it can cause serious eye damage. Protection from possible eye damage is the responsibility of each and every student in the laboratory. The following guidelines should be applied.
(a) NEVER LOOK DIRECTLY INTO THE LASER BEAM!
(b) Do not pick up or otherwise make large adjustments in the position of the laser while it is turned on.
(c) Do not allow the beam to cross an aisle where people may be walking or to cross from one side of the bench to the other where someone may be seated.
(d) Watch for beams reflecting off glass or other shiny surfaces. They can be as dangerous as the main beam.
(e) The lasers are normally be placed on the laboratory benches at approximately eye level for any persons seated in the chairs. Because of this, be careful that your laser does not shine across the bench to the other side. Also, be sure to place the large wooden box across the bench at its midpoint so that the beam cannot travel the entire length of the bench.
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Diffraction & Interference Experiment 112-6
PROCEDURE
1. Single Slit Diffraction
The laser should be mounted on a rod and lab stand assembly and placed at the end of the lab bench. Mount the slide on a laboratory stand using a stem-mounted spring clip holder and a right angle clamp to hold and position it about a centimetre in front of the laser.
Tape a 40 cm strip of paper tape horizontally at the same height as the laser to the wooden screen placed about half way down the lab bench. Measure the distance D between the slit and the screen.
Qualitatively observe the effect of slit width on the diffraction pattern displayed on the screen by shining the laser through each of the slits.
Shine the laser through the second narrowest of the single slits and adjust its position of to optimize the diffraction pattern both for symmetry and intensity of illumination. Mark the location of the central maximum (CM) and of every diffraction maximum observable on both sides out to n = 20.
Remove the paper tape from the screen. Label the CM and number the diffraction minima. Measure the distance sn between six pairs (same value of n) of diffraction minima on opposite sides of the CM.
Record your data in a table similar to the one below and calculate the average value of the slit width as well as the standard error in the mean.
n
()3 10 mns?×
(rad)n?
()