Experiment 16 Diffraction and Interference of Light

Transcription

1 PHYSICS EXPERIMENTS Experiment 16 Diffraction and Interference of Light WARNING: Laser light can damage the retina. Keep the laser level at all times to avoid shining the light into an eye either directly or off of a reflecting surface. In this experiment you observe the patterns formed by laser light after passing through different types of openings. The patterns, observed far behind the openings, consist of definite distinct areas of light and dark. The spatial variations in light energy arise from the constructive and destructive interference of light waves. The spatial distribution of energy in an interference pattern allows precise determination of the size and shape of the opening the light passes through, essentially allowing very precise distance measurements in terms of numbers of light wavelengths. Preliminaries. Light is an electromagnetic wave. It has the wave properties of amplitude, frequency, wavelength, and speed. As with any wave, the Principle of Superposition describes the treatment of multiple light waves overlapping in space. If the light waves overlap in phase, differing by an integer number of complete wavelengths, constructive interference results and bright areas appear. If the light waves overlap out of phase, differing by an odd integer number of half wavelengths, destructive interference results and dark areas appear. There are many ways to get light waves to overlap in space. The most basic is to send a single light wave through an opaque screen with transparent slits in it. Each slit in the screen becomes a wave source. Waves from the slits overlap in the region behind the screen, where a distinct diffraction pattern of interference maxima (bright, constructive interference) and minima (dark, destructive interference) appears. The distribution of light in a diffraction pattern depends on the wavelength λ of the light as well as the features of the screen (width of slits, distance between slits, number of slits, etc.). When light travels through a screen whose features are well known, the diffraction pattern may be used to determine the wavelength of the light. Screens used for this purpose are called diffraction gratings. Diffraction gratings consist of many narrow, evenly spaced slits. The many slits increase the amount of destructive interference, so that the constructive interference regions are very distinct and their positions easy to precisely measure. The change in the diffraction pattern as more slits are used is shown in Figure 1. two slits three slits seven slits Figure 1. Diffraction patterns for different numbers of slits. Usually the distance between the lines in a diffraction grating is specified by its reciprocal, the line density ρ. This value is usually expressed in units like 1/mm. The use of diffraction patterns to determine wavelengths of light sources is known as spectroscopy. This is an extremely important diagnostic tool for identifying materials, as the distribution of wavelengths is distinctive and acts like a fingerprint. If the wavelength(s) of the light source is well known, the diffraction pattern may be used to determine the features of the screen. Here, the light is being used as a ruler, with the wavelength being the ruler divisions. The wavelength of visible light is roughly tenths of micrometers (10-7 m), so that measurements of length by diffraction analysis are roughly one thousand times more precise than those using an ordinary meter stick.

2 16-2 PHYSICS EXPERIMENTS 132 The light sources used in this experiment are lasers. Lasers produce narrow beams of light at, essentially, a single wavelength. This simplifies the diffraction pattern analysis. Figure 1 shows that the locations of the interference maxima are independent of the number of slits in the diffracting screen (although the width of the maxima does change). The maxima locations are positions of constructive interference where light waves from adjacent slits arrive at the viewing screen an integer number of wavelengths apart, as shown in Figure 2. incident wave where m = 0, 1, 2, 3 is the order number. Some basic trigonometry applied to Figure 2 shows that a feature in the interference/diffraction pattern at angular position θ appears on a viewing screen at distance y from the center of the pattern given by y = R tan" (eq.2) where R is the distance from the slide to the viewing screen. y m = 1 d m m = 0 d sin = m m R screen m = 1 Figure 2. Constructive Interference between Adjacent Slits When light of wavelength λ travels through a diffraction grating (or a double-slit) with slit spacing d, the interference pattern has maxima (bright spots) at angular position θ m given by d sin(" m ) = m# (eq. 1) When eq. 1 and eq. 2 are applied to the central part of the diffraction pattern, characterized by angular position θ < 15 0, the small angle approximation " # tan" # sin" where θ is expressed in radians can be used to a precision of two significant figures. In this case, the interference maxima are evenly spaced at a distance Δy given by Δy=λR/d (eq.3)

3 PHYSICS EXPERIMENTS The discussion above is concerned with light waves originating from different slits. Light coming through a single slit can also show interference. This is because each point on the slit can be thought of as a wave source. The light passing straight through the slit will produce a bright central. The first minimum on either side of this central will occur when the light from the upper half of the slit interferes destructively with the light from the lower half. This condition is: and 2 are out of phase by λ/2 then rays 2 and 3 will also be out of phase by λ/2, or (a/2) sin θ = λ/2. The pairs of rays will therefore interfere destructively to produce a minimum. a sin θ =λ (eq.4) incident wave y first minimum 1 2 a 3 central a sin = screen light intensity pattern where a is the slit width, λ is the wavelength, and θ is the angular position of the minimum as indicated in Figure 3. on the next page. This Figure shows that, for every ray leaving the upper half of the slit, there is a corresponding ray from the lower half which will be λ/2 out of phase when the two rays combine at the first minimum position. If rays 1 R first minimum Figure 3. Diffraction through a Single Slit Note: Eq. 1 and eq. 4 are identical in form but refer to quite different physical situations. Eq. 1 identifies interference maxima for multiple slits, while eq. 4 identifies an interference minimum for a single slit.

4 16-4 PHYSICS EXPERIMENTS 132 In this experiment a spectroscopic analysis of laser light using a grating is performed to determine the wavelength of the laser. Subsequently, the known wavelength of the laser is used in a diffraction pattern analysis to determine slit widths and slit spacings. Procedure. Part A. Diffraction Grating Pass the laser beam through the diffraction grating. Make sure that the beam is perpendicular to the grating and to the viewing screen. Move the grating closer to the viewing screen. Observe the effect of the change in distance on the pattern on the viewing screen. Return the grating to its original position. Find the manufacturer specified line density ρ of the grating. Record the value. Measure and record the distance R from the grating to the viewing screen. Measure the distance y 1 from the center dot to the one immediately next to it on the left. Measure the distance from the center dot to the one immediately next to it on the right. These distances should be the same. If they are not, take the average and record it. Calculate the line spacing d for the grating from the line density. Calculate the wavelength λ of the laser using eq. 1 and eq. 2. Part B. Single Slit Shine the laser through the single slit. Make sure that the beam is perpendicular to the viewing screen and to the slide containing the slit. Measure and record the distance R from the slit to the viewing screen. Record the distance 2y 1 from minimum to minimum on either side of the central. Turn off the lights to make sure find the minima. Calculate the slit width a. Use the standard value of λ= nm for the red laser wavelength. Part C. Double Slit Shine the laser through the more closely spaced double slit. Make sure that the beam is perpendicular to the viewing screen and to the slide containing the slits. Measure and record the distance R from the slits to the viewing screen. Record the distance Δy between maxima around the center of the pattern. Think about the best way to do this in view of the discussion above eq. 3. Turn off the lights to make sure find the maxima and minima. Calculate the slit spacing d. Use the standard value of λ= nm for the red laser wavelength. Questions (Answer clearly and completely). 1. At the position of the corresponding to m=4 in eq. 1, how much further has the light ray from one of the slits traveled compared to the light ray from the slit next to it? from the light ray two slits away? Consider Figure 2 carefully. 2. How does the pattern change as the distance between the grating and viewing screen changes? What does this indicate about how light energy exits the grating? 3. What value do you determine experimentally in Part A for the wavelength of the laser light? The red laser wavelength is very well known to be λ= nm. Determine the percent difference of the experimental value from the standard value. 4. In Part B, you are asked to measure from minimum to minimum rather than from center to minimum? Why? Is this a good idea?

5 PHYSICS EXPERIMENTS What value do you determine experimentally for the width of the slit? 6. The ideal double slit diffraction pattern consists of interference maxima which are all equally bright. Is this what you observe? Describe/sketch carefully what you do observe. Explain why you see what you do see? [Suggestion: look at the single slit pattern again.] 7. What value do you determine experimentally for the distance between the centers of the slits in the double slit?