THE EXPERIMENT

You will study here the diffraction of light emitted by a low-power Helium-Neon laser. The power of the beam from this unit is abut one milliwatt (10^-3 watt), which is, under most conditions, not hazardous. This means, specifically, the following:

• Small amounts of the beam reflected from ordinary objects, or even shiny objects not having flat, mirrorlike surfaces, will not damage the eyes, even though the reflections can seem uncomfortably bright.
• However, you can damage your eyes by looking directly into the beam, or a beam reflected by a flat mirror: the level of damage is probably less than would occur if you look at the sun on a clear day at noon. Exercise reasonable caution!
• When handling such objects as flat glass slides, or even film slides, be careful that they remain approximately perpendicular to the beam when in the beam, so you do not receive accidental eye exposure from reflections. Exposure in this case is probably not damaging, but again, very uncomfortable.

Equipment

1. The laser
2. An "optical bench", which is a metal rail upon which the holders for various pieces of equipment are clamped,
3. Holders for the slides that hold the diffracting objects,
4. A variety of electron beam etched slides that contain very small patterns or apertures whose diffraction patterns are the object of your study.

Procedure

A. Measurement of light wavelength, multiple slits

In obtaining a measurement of the laser wavelength, you will now have a chance to do a much more refined version of the two-slit interference experiment previously done using microwaves (Exp. 5).

Recall that for two slits, one finds a maximum in the signal strength when

sin = ,

where d is the slit spacing. At this angle, we see from Fig. 6 that the two paths from the screen differ by an integral number of wavelengths, and so, if the light waves are in phase coming out of the slits the two contributions are also in phase along direction .

Figure 6

1. Turn on the laser on your optical bench and position the laser approximately 2 meters from the wall of the lab. You will hold your lab book against the wall to transfer images onto the pages of your book.
2. Next, take the slide labeled 1C on its frame, and place it on the magnetic holder. With the labels horizontal, adjust the slide so that it is near the front of the laser, with the laser beam passing approximately through the two slit group labeled 0.04 mm width, 0.125 mm spacing.
3. Now, by moving the slide laterally, and moving the slide vertically if necessary, you should find a location where a horizontal row of spots appear on the screen. Here, the light is passing through a pair of parallel slits. By using the relation

sin = , n = 1, 2, . . .

or,

x = (L) = nL

for spot separation from the screen center, you can estimate the value of (with uncertainty). The value of d which you will need is marked on the slide (0.125 mm). Compare the experimentally determined value of with the actual value of ₀ = 632.8 nm.

1. Now, move the slide laterally so that the beam passes through the slide on the other side labeled 5 slit. You should once again get a row of spots, but now, the pattern is produced by a set of 5 evenly spaced slits. What difference is there in the character of the maxima? How do you account for a larger number of slits making this difference?

Once again, by measuring the displacement of these spots from the screen center, estimate , and compare to the actual value of ₀.

NOTE: a complication due to diffraction effects may cause some confusion. Read part D of this sequence before completing part A.

B. Single Slit Diffraction

You can verify your wavelength measurements in Part A and check the properties of a single slit diffraction pattern by using the slide marked "1A". The second slit, marked .04 mm, is the one which would correspond to the slit width used in Part A. The simplest thing to test is the location of minima (which will need a darkened viewing room) as described following Eqn. 2. The intensity plot which is supposed to describe the diffraction pattern is shown in figure 3. Try to locate the first and second minima ( = and 2) and check the value of (with uncertainty) which this gives. Compare this value of to those obtained in part A, and to the actual value of ₀.

An alternative to finding minima would be to locate the first maximum away from beam center:

max of tan = (radians) ( = 4.5, 7.73, etc.)

These values of can also be used to find the wavelength from the angular location of the maxima.

C. Diameters of Thin Strands

Through the use of Babinet's principle and the single-slit diffraction pattern, it is a simple matter to measure the diameters of very thin filaments.

You will be supplied with samples of two sizes of very fine wire. Place a strand of each of these in the beam near the laser, and by measuring the diffraction pattern, infer its diameter (with uncertainty). Your result can be checked against wire tables, which list diameters for the given gauge numbers.

Another interesting measurement is that of the diameter of human hair. Much of the interest lies in the variation of hair thickness among individuals, so don't hesitate to solicit samples from everyone around you. Consider possible correlations between color and thickness, for example.

D. Two Dimensional Arrays

In this experiment, we employ a very fine-mesh screen of a kind used in photo-engraving. Samples of this screen are mounted in the slides marked 1D (rectangular array). You will notice that your unaided eye can hardly tell that it is a screen at all.

In order to understand the diffraction pattern of this screen, we will once again consider the pattern from a simple system of two slits, such as you used with microwaves in Exp. 5, or with laser light in the first section of this experiment.

Suppose the slits are spaced a distance d apart (center-to-center), with each having a width a, where we suppose also that d is much greater than a. As we have learned, the interference pattern from the pair of slits will be an array of spots, separated by an interval

y = L ,

where L is the slit-to-screen distance.

However, each of the slits also produces its own diffraction pattern, and that is a system of spots that obey the function given by Eqn. 2,

I = I₀ ² ,

where = ,

in the limit of small (or L >> y). The zeros of this function occur at y=nL/a for integer n, and so, the interval between zeros is

y = L .

The result of superimposing the diffraction patterns of the individual slits and the interference pattern they produce in combination is to produce a composite pattern as represented below:

Figure 7

Thus, by measuring both the intervals between interference peaks and diffraction peaks (or minima), one can determine both d, the slit spacing, and a, the slit width.

In the present experiment, we may now employ the principles outlined above, together with Babinet's principle, to determine both the mesh interval of the screen sample and the actual thickness of the strands. Be sure to include and propagate the errors in your measurements. You will find the diffraction pattern from this screen quite bright and easy to measure.