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Single and Double Slit Experiments Overview

In this module, you'll learn about interference and diffraction of waves.

Objectives:

After completing Module 5 activities, you will be able to:

· Describe the differences between interference and diffraction.

· Describe qualitatively how single and double slit diffraction gratings produce diffraction patterns.

Assignments:

1. Single and Double Slit Experiments Lab Submission

Key Terms:

· Transverse Wave

· Longitudinal Wave

· Interference

· Diffraction

· Single Slit Experiment

· Double Slit Experiment

Single and Double Slit Experiments Background

In order to fully understand the single and double slit experiments, the first step is to appreciate what waves are and why they are important. For the purpose of this lab, there are two types of waves to consider: transverse and longitudinal:

Transverse and Longitudinal Waves

A simple wave consists of a periodic disturbance that propagates from one place to another. The wave in Figure (Links to an external site.)propagates in the horizontal direction while the surface is disturbed in the vertical direction. Such a wave is called a transverse wave or shear wave; in such a wave, the disturbance is perpendicular to the direction of propagation. In contrast, in a longitudinal wave or compressional wave, the disturbance is parallel to the direction of propagation. Figure (Links to an external site.) shows an example of a longitudinal wave. The size of the disturbance is its amplitude X and is completely independent of the speed of propagation vw

The figure shows a woman holding a long spring in her hand and moving it up and down causing it to move in a zigzag manner away from her. It is an example of a transverse wave, the wave propagates horizontally. The direction of motion of the wave is shown with the help of right arrows at each crest and trough.

In this example of a transverse wave, the wave propagates horizontally, and the disturbance in the cord is in the vertical direction.

The figure shows a woman standing at left pushing a long spring in to and fro motion in horizontal direction away from her without moving her hand up and down. The cord stretches and contracts back and forth. This is an example of a longitudinal wave, the wave propagates horizontally. At some points the spring is compressed and at some other points the spring is expanded. One contracted part is equal to the amplitude X.

In this example of a longitudinal wave, the wave propagates horizontally, and the disturbance in the cord is also in the horizontal direction.

Waves may be transverse, longitudinal, or a combination of the two. (Water waves are actually a combination of transverse and longitudinal. The simplified water wave illustrated in Figure (Links to an external site.)shows no longitudinal motion of the bird.) The waves on the strings of musical instruments are transverse—so are electromagnetic waves, such as visible light.

Sound waves in air and water are longitudinal. Their disturbances are periodic variations in pressure that are transmitted in fluids. Fluids do not have appreciable shear strength, and thus the sound waves in them must be longitudinal or compressional. Sound in solids can be both longitudinal and transverse.

The figure shows a guitar connected to an amplifier and a man holding a sheet of paper facing the speaker attached to the amplifier. The strings of the guitar when played cause transverse waves. On the other hand, the sound of the guitar creates ripples on the sheet of paper causing it to rattle in a direction that shows that the sound waves are longitudinal.

The wave on a guitar string is transverse. The sound wave rattles a sheet of paper in a direction that shows the sound wave is longitudinal.

Earthquake waves under Earth’s surface also have both longitudinal and transverse components (called compressional or P-waves and shear or S-waves, respectively). These components have important individual characteristics—they propagate at different speeds, for example. Earthquakes also have surface waves that are similar to surface waves on water.

Diffraction and Interference

There are two wave properties that are important: diffraction and interference. Diffraction can be defined as the spreading out of a wave due to its passing through a small opening. A simple example of diffraction of light is shown in this image taken from a student winner of an AAPT High School Physics Photo Contest (click here (Links to an external site.) to view).

A good visual representation of the process of diffraction through different gap sizes can be found here (click to load) (Links to an external site.).

The other property is interference. This occurs when more than one wave interact at a specific location. The interference can be constructive (waves in phase such that high intensity regions align with one another) or destructive (waves out of phase where high and low intensity regions cancel one another).

The link included here (click the link) (Links to an external site.) discusses both constructive and destructive interference for a transverse wave. Time should be spent on this link so that you are comfortable with exactly what is taking place. This is a key factor in the double slit experiment, which will be the focus for the second part of this lab. For further reading on interference, the following page from Physics Classroom is recommended (Links to an external site.).

For the single slit experiment, only diffraction is important. This is because a single wave is spreading out and there is no overlap. The following link (click to view) (Links to an external site.)provides a good explanation of diffraction, and shows how waves combine to form the diffraction pattern.

Fig. : Diffraction from a slit. Above is given the value of the wavelength of the incident light and the slit width (1 nm = 10-3 micron). The figure was obtained from applet java: " Single-Slit Diffraction (Links to an external site.) ". (Credit: Sergey Kiselev e Tanya Yanovski-Kiselev

Notice in the image that there is a very bright central maximum with small oscillations to either side. For the purpose of this lab we are simply going to concentrate on the strong central maximum. The brightest part of the image occurs directly across from the center of the slit (no diffraction … the path of light has no deviation). Now notice that moving to either side causes a reduction in light intensity. This can be thought of as a decrease in intensity as the diffraction angle increases.

For the double slit experiment both diffraction and interference are important, as now there are two waves that interact with one another.

The figure contains three parts. The first part is a drawing that shows parallel wavefronts approaching a wall from the left. Crests are shown as continuous lines, and troughs are shown as dotted lines. Two light rays pass through small slits in the wall and emerge in a fan-like pattern from two slits. These lines fan out to the right until they hit the right-hand wall. The points where these fan lines hit the right-hand wall are alternately labeled min and max. The min points correspond to lines that connect the overlapping crests and troughs, and the max points correspond to the lines that connect the overlapping crests. The second drawing is a view from above of a pool of water with semicircular wavefronts emanating from two points on the left side of the pool that are arranged one above the other. These semicircular waves overlap with each other and form a pattern much like the pattern formed by the arcs in the first image. The third drawing shows a vertical dotted line, with some dots appearing brighter than other dots. The brightness pattern is symmetric about the midpoint of this line. The dots near the midpoint are the brightest. As you move from the midpoint up, or down, the dots become progressively dimmer until there seems to be a dot missing. If you progress still farther from the midpoint, the dots appear again and get brighter, but are much less bright than the central dots. If you progress still farther from the midpoint, the dots get dimmer again and then disappear again, which is where the dotted line stops.

Fig: Double slits produce two coherent sources of waves that interfere. (a) Light spreads out (diffracts) from each slit, because the slits are narrow. These waves overlap and interfere constructively (bright lines) and destructively (dark regions). We can only see this if the light falls onto a screen and is scattered into our eyes. (b) Double slit interference pattern for water waves are nearly identical to that for light. Wave action is greatest in regions of constructive interference and least in regions of destructive interference. (c) When light that has passed through double slits falls on a screen, we see a pattern such as this. (credit: PASCO)

This diagram needs a bit more analysis. Notice the horizontal line drawn to the right from the midpoint between the two slits. Follow this line to the right and you see that it is aligned with a bright region. Moving upward or downward from this bright region there are several alternating dark and light regions. The pattern that you see to the far right is then the result of the constructive and destructive interference.

Note: Some of this material is from OpenStax College Physics.

Download for free at http://cnx.org/contents/031da8d3-b525-429c-80cf-6c8ed997733a@9.99.