# The Wave Nature of the Electromagnetic Spectrum

NOTE

This manual describes the laboratory experiment used during the 1996 - 1997 academic year. Significant changes have been made since then, and the manual used during the current academic year is in NOT available yet on the WEB. Hardcopies can be purchased at the bookstore.

## Purpose

To observe interference patterns, and calculate the wavelength of a helium-neon laser and microwave radiation..

## Prelab Homework

The prelab homework must be done at home and handed to the lab TA before you start the lab. Read the instructions for this lab.

## Question

• Derive an expression for from the equation using the method indicated in the Error Analysis section of the lab manual.

## Introduction

The prevailing view of the nature of light has changed several times in the past three centuries. Newton described light as a stream of particles, partly because of its property of straight line travel. In the 19th century, the notion that light consists of waves came into acceptance. In this century it has been shown that light behaves or more generally any part of the electromagnetic spectrum with both particle-like and wave-like properties. One method of observing this wave nature characteristic is through the interference and diffraction of electromagnetic radiation.

These experiments utilize a helium-neon laser of low power ( ). The beam of radiation is monochromatic (of a single wavelength), coherent (in exactly the same phase-step), and parallel.

CAUTION: Do not look directly into an undispersed laser beam or allow it to fall on your eyes.

## The experiment

### Part I: Double-slit Interference

For this part you will use the laser, the "multiple slit" slide, a screen, and a ruler to determine the wavelength of the laser radiation.

• Using the microscope, carefully determine the separation of the two slit image on the film. Measure to an accuracy of about the nearest ten-thousandths of an inch or a few thousandths of a millimeter. If necessary, convert your result to centimeters.

Turn the screw in only one direction to avoid `backlash' errors. Your lab assistant will help you. [This measurement does not need to be made first. Since there is only one microscope, you may want to wait a while to avoid the queue.]

• Install the slit in the holder and place it in front of the laser. Aim the laser at the double slit portion of your slide.

Figure 13.1

• Place the screen at the other end of the table from the laser. When the laser is turned on, a series of (dim) parallel, vertical fringes will be seen on the screen. The spacing of the fringes(y) depends on the screen-slit distance L the slit separation d and the wavelength given by the equation,

(13.1)

Assuming that . This is shown in Figure 13.2.

• Sketch the fringes on your data sheet. The brightest fringe on the screen, at , in Figure 13.2, is called the zero-order fringe because the path-length difference to from each slit is zero. The next adjacent fringes on each side are the first-order fringes and the path-length difference equals one wavelength, the next are second-order fringes and so on.

• Measure the separation(y) of two corresponding fringes. Be sure that you measure the center-to-center distance rather than the edge-to-edge distance. And measure the separation of six or eight fringes, divide by the number of fringes measured and find the average separation of two adjacent fringes. Because the fringes are not sharp lines, you may want to make several measurements.

• Finally, measure the distance L from the slits to the screen. Then use L, d, and y to calculate the wavelength of the laser light. Compare your experimental value of to the actual value of 632.8 nm. Calculate ,using the formula calculated in the prelab.

### Part II: Multiple Slit Interference

#### Procedure

• Aim the laser at the "three-slit" part of the slide. When the laser is turned on as before, an interference pattern is produced on the screen.

• Sketch to scale the appearance of the interference pattern you see on the screen. Use shaded bars or lines to indicate the bright fringes. In your sketch, identify the zero-order fringe. Draw the scale of the interference pattern on your sketch so that you can compare it to the fringe patterns produced by other slit combinations.

• In turn, use each of the four, five, and six-slit gratings. Sketch the appearance of each of these fringe patterns to scale.

• What happened to the interference pattern as the number of slits increased?
• Without measuring, do all the slits on all of the slides have equal separation? How can you tell?
• Try the one slit. Discuss your results.

### Part III: Other Interference Patterns

#### Procedure

• Place the screen(as in screen window) in the holder in the beam of the laser.

• Sketch the appearance of the interference pattern; explain your observation.

If you have a hypothesis to explain the screen interference pattern, check it with appropriate combinations of multiple slit slides.

### Part IV: Microwave Double-Slit Interference

For this part, we demonstrate the wave nature of a different part of the electromagnetic spectrum. In the next room, use the microwave transmitter and receiver apparatus to determine the wavelength of microwave radiation. As in the optical counterpart, interference fringes will be produced by the double slit. Here, however, the separation of the fringes will be measured as an angle, not a displacement. The receiver has a meter used to measure the intensity of the radiation received.

#### Procedure

• Use calipers to determine the separation of centers of the double slit. Record this value, d.

• Install the slits on the turntable at the center, between the transmitter and the receiver horns.

• Align the slits so that they are normal (perpendicular) to the transmitter.

• Reset the protractor scale so that its 180deg. mark is at the indicator for the transmitter.

• Move the receiver five degrees in either direction, and record the angle and meter reading.

Figure 13.2

• Proceed in this fashion, moving the receiver five degrees in the same direction, away from 0deg., recording each angle and meter reading.
• When you have obviously passed through the two maxima on each side of the 0deg. mark, s t o p.

#### Data Analysis

• Graph the amplitude vs. .

• As the angle varies, the path length difference . If is an integer number of wavelengths then constructive interference will occur, and a maximum of received power will be seen. The equation is,

(13.2)

where is the wavelength and m is an integer.

From the graph, estimate the angular separation between two adjacent fringes. Record this value. Using the measured value of d, calculate the wavelength .

Figure 13.3

### Part V: The Hologram(demonstration by TA)

One of the most promising applications of continuous laser light is its ability to make three dimensional photographs called holograms. A hologram is made by exposing photographic film to a scene which is wholly illuminated with laser light. The film is simultaneously exposed to a reference beam that comes directly from the same laser. As the light from the laser and the scene falls upon the film, an interference pattern is recorded. The film is then developed to give a negative, which is the hologram. See Figure 13.4.

As you look at the hologram itself, the light and dark streaks and smudges you can see are not the places where the "information" is recorded. To see the interference pattern one needs to look at the hologram through a high magnification microscope. (The light and dark streaks and smudges are just that --streaks and smudges.)

To view the scene, shine a light of the same wavelength on the hologram and look through it. In fact, two images are produced. One of them is virtual and behind the hologram, and the other is real and in front of the hologram.

It is relatively easy to see the virtual image. Look through the hologram from the position indicated on the desk. You should be able to see a three dimensional scene which was recorded on the hologram. If you move your head from side to side and up and down, you should be able to see the objects from different perspectives, just as you would if there were an actual group of real objects in front of you.

Figure 13.4

Make a hole about 1cm in diameter in the center of a sheet of note paper and move this over the face of the hologram while looking through it at the 3-dimensional scene. Notice that any portion of the hologram contains complete information for viewing the entire scene. However, there are some differences in the quality of the scene as you view through various portions of the hologram.

Figure 13.5

It is not very easy to see the real image which is projected in front of the hologram. Try to see the real image by looking from the position indicated. If you move your head from side to side and up and down you may possibly be able to tell that something is there, although the images will be confused. Try and determine whether the real image is inverted or erect, magnified or reduced.

## Question

• Holograms are usually made with lasers, as lasers are single wavelength, coherent, and parallel light sources. This easily demonstrates the principle of constructive interference. However, holograms can be made from "white light." Why? (Hint: In lab you saw a hologram made from white light, if you moved around the image it changed colors (i.e. blue, green, red, yellow.)

Send comments, questions and/or suggestions via email to wolfs@nsrl.rochester.edu.