Interference and diffraction

Purpose

To study basic properties of light interference and diffraction using a laser.

Equipment

Helium-Neon Laser, diffraction grating, an assortment of 5 mounted slits, protractor, stand for slits, meter stick, ruler.

WARNING: Never look directly into the laser or its specular reflection!

Preliminary Discussion

I. Lasers

An atom can absorb a photon by raising an electron from the ground state to an excited state. A short time later, spontaneous emission takes place, and the excited atom returns to its ground state by emitting a photon, which has energy equal to the energy level difference between the excited and ground states. The direction and phase of these spontaneously emitted photons are completely random, which renders them useless if one wants a directed beam of light.

Albert Einstein proposed an idea he called stimulated emission of radiation, which is the basis for all laser light emission (laser is the acronym for Light Amplification by Stimulated Emission of Radiation). He reasoned that if a photon with the same frequency as the spontaneously emitted photon scattered from an atom that was in its excited state, the atom could release a photon identical to the first in frequency, direction, phase and polarization. The two photons are thus, coherent.

The atoms inside a laser tube have to be brought to the necessary excited state independently of the photons. This process of raising atoms to a higher energy level is known as "pumping". Lasers can be pumped in several different ways. The helium-neon lasers work by applying a high voltage across the laser tube. This causes the helium inside the tube to absorb energy. After gaining energy, a helium atom eventually collides with a neon atom, which absorbs the energy that was contained in the helium atom. The neon atom then spontaneously emits a photon, which produces red light. This light corresponds to the strongest and most visible of the wavelengths of light your helium-neon laser emits.

For a continuously emitting laser, though, a majority of the atoms must be pumped to an excited state, that is, there must be a population inversion. This characteristic is maintained by pumping atoms at the same rate energy is lost. Also, two mirrors are used to amplify the beam. One mirror is almost totally reflective while the other is about 99% reflective. These mirrors are placed at opposite ends of the laser tube. This is done so that the photons emitted along the axis of the tube can then reflect back and forth through it, so that they may have a much higher chance of colliding with an excited atom than light traveling in other directions. This increases the number of photons stimulated along the axis of the tube on each pass. About 1% of the light passes the aperture on each reflection and forms the coherent laser beam.

Laser light is highly directional, monochromatic and very bright. It is directional because only the light traveling parallel to the long axis of the laser tube is amplified by stimulated emission, multiple times. The monochromaticity of a helium-neon laser emission occurs because of the single transition energy yielding visible photons. The high intensity is due to the large number of sources emitting in coherence.

II. Light - Interference and diffraction

For two slits separated by distance d (as sketched in Figure 1), light will destructively or constructively interfere on a screen placed far from the source.  This will look like a pattern of bright and dark fringes.  Light from either slit arriving along the centerline between the two slits constructively interferes with the light from the other slit, because they travel the same distance.  Thus there is always a central maximum in brightness.  As is seen in Figure 1, for light not on the centerline, the light travels different distances and the path length difference is d sin(q), where q is the angle to the position of interest on the screen.  The first maximum beside the central maximum occurs when the path length difference d sin(q) = l (the light wavelength). Additional maxima occur at larger angles when d sin(q) = ml, where m is an integer m = (1, 2, 3...).  For destructive interference, d sin(q) = (m+)l, where the light from the two slits is out of phase.

For a single slit of width w, light from different parts of the slit interferes, either destructively or constructively. This is called single slit diffraction. The condition for a minimum in intensity (a dark fringe) is w sin q = ml. If there are two or more slits, you can observe the single slit diffraction pattern superimposed on the multiple slit interference pattern. Typically the width of each slit w is much less than the spacing between slits d, so the single slit diffraction pattern is broader than the multiple slit interference pattern.

When there are more than two sources, constructive interference still occurs when the path length difference for neighboring sources is ml, so the formula  applies for constructive interference from multiple sources, where d is the distance from the center of one line to the next.  For multiple slits, there may be smaller intensity maxima at angles in between those that give perfect constructive interference.  For example, for three slits each separated by d, the first completely constructive interference maximum occurs for .  But, there is a small maximum when because light from the first and third slits constructively interferes while light from the middle slit only destructively cancels part of the light from the first and third. 

Diffraction gratings have thousands of lines per inch patterned onto a film. The gap between each line acts as a source.  Again, the maxima obey the formula , but now, there are no intermediate maxima at smaller angles.

III. Experimental Work

Measuring something very small.

By using the properties of interference and diffraction, it is possible to make very accurate measurements of small holes or spaced lines.  You should shine the laser beam through the slits onto the wall opposite your bench.

The configuration of each slit set is shown schematically in Figure 2.

Using a slide with a single slit on it, measure the width of the slit w by applying the formula w sin q = l, where w is the slit width and q is the angle from the slit to the first minimum in intensity and l is the wavelength of the laser 632.8 nm (see figure 1). You can measure the angle q by measuring the distance L from the slit to the central spot of the laser on the wall, and measuring the distance y on the wall, from the central spot to the first minimum in intensity. Then, by definition, tan q = y/L.  If the angle is small, y/L will also be equal to sin q and also q = y/L (measured in radians).  So, once you have measured q, solve for w.

Using a slide with double slits, find the spacing between the slits d by using d sin q = ml.  q is the angle to the mth maximum.  Also, determine the width of each slit by measuring where the two-slit interference pattern intensity diminishes to zero due to diffraction from each slit and applying the single slit diffraction formula above.

Using three slides with more than two slits, find the spacing between each slit for each slide by again applying d sin q = ml, and find the width of each slit using w sin q = l (this may become quite difficult when there are many slits).  Are there any subtle intensity variations between the major intensity maxima?  Make a sketch of the intensity as a function of position starting at the central peak and moving out to one side, past the first order maximum.

The diffraction grating is essentially many slits, usually called lines. It looks almost transparent but if you look through it at white light, you may be able to see a rainbow of colors (why?). Put the diffraction grating in your slit mount. Note that the diffraction spots are at much larger angles. By once again applying d sin q = ml, find the spacing between lines on the grating, and the inverse, the number of lines per centimeter.


This page last updated on 19 February 2002.
1996 Dr. H. K. Ng, 2000–2002 D. H. Van Winkle.
All Rights Reserved.