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PHYS 201 LAB 01
Interference and Diffraction Using Visible Light
1. Objective
The objective of this experiment is to show that light can exhibit wavelike properties such as interference and diffraction.
2. Theory
NOTE: The theory used in this lab is covered in Chapter-33 of your textbook.
2.1 Introduction
If two or more waves of light of the same frequency overlap at some point in space the resulting effect produced depends both on the phases and amplitudes of the two waves. This phenomenon, called interference, can not be explained on the basis of ray optics or the corpuscular nature of light – the wave nature of light must be explicitly invoked.
Two sources of light are called coherent if they emit light waves of the same frequency and the emitted waves have a constant phase relationship between them. Light radiating from coherent sources is also called coherent light. Thus light from such sources as a lightbulb, a candle or a star is incoherent. As described in your textbook, light waves are transverse waves. To observe interference on the laboratory time scale using light waves an additional condition must be imposed – the two interfering waves must have the same polarization. One way to produce such two coherent waves is to use radiation from two different parts of the same wavefront.
We will use the following notation for variables in this experiment:
a = width of slit(s) d = distance between two slits in double-slit experiments y = position of light sensor relative to center of interference pattern θ = arctan( y / L ) = diffraction angle of light at position y
The diffraction angles involved in this experiment are small enough that we will assume throughout that sin(θ) = tan(θ) = θ. Therefore we can write simply θ = y / L.
The following symbols indicate constants for the experiment:
λ = wavelength of laser light = 650nm L = distance from slit(s) to light sensor = 80cm
2.2 Double-Slit Interference Theory
Consider two point sources S 1 and S 2 of coherent light as shown below. The light waves from each slit will spread out in all directions. At a particular point on the viewing screen, the light waves from the two slits will interfere in a way that depends on their phases difference.
If the two waves depicted in the diagram are in phase when they strike the target, we expect constructive interference to produce a bright fringe, where the intensity is maximum. If the two waves are out-of-phase, we expect a dark fringe, where the intensity is minimum. We can approximate the path difference between the two waves with the geometric construction shown below:
If L is much larger than d , then geometrically, we can approximate that δ ≈ d sin(θ). For a particular angle θ, we expect constructive interference to produce an intensity maximum if the path difference δ is an integer multiple of λ. By the same reasoning, we expect minima to occur when δ is a half-integer multiple of λ. Therefore we expect bright and dark fringes to occur at the following angles:
16, 32, etc. point sources. Therefore if m is any nonzero integer, we can write: This derivation was not very rigorous, but this formula does gives the location of single- slit intensity minima in the limit that L is much larger than a. Again using the small-angle approximation and plugging in the known values of L and λ, we have:
In the double-slit experiments, both effects will be at work: diffraction of light through each slit and interference from the two separate slits. The observed double-slit pattern will have minima corresponding to both formulas, and the pattern itself will look like this:
The Fraunhofer pattern formed by diffraction at each slit acts as an “envelope” which limits the amplitude of the intensity fringes formed by double-slit interference.
3. Experimental Details
The experiment is divided into two parts:
In Part 1 (Single Slit Diffraction) , we shine laser light through a single slit and analyze the resulting diffraction pattern on a target behind the slit. This is done for two
slits of different sizes. In Part II (Two-Slit Interference) , we shine light through two identical slits and analyze the resulting interference pattern. The distance between slits is varied to observe changes in the interference pattern. Below is the summary of the two experiments and their corresponding parameters.
Summary of Experimental Parameters
Part I – Single Slit Diffraction
a = 0. 16 mm a = 0.08 mm
Part II – Double Slit Interference
a = 0.04 mm, d = 0.25 mm a = 0.04 mm, d = 0.50 mm
BEFORE YOU BEGIN: IMPORTANT PRECAUTIONS
- Do not look directly at the laser. Doing so may lead to permanent damage to your eyes.
- Handle the linear translator / light sensor assembly with care.
3.1 Apparatus
The apparatus consists of the following components, as viewed from above:
The light sensor and rotary motion sensor are mounted on a rack assembly called the Linear Translator. The concept is simple: a laser shines onto one or more slits and the resulting light strikes a target 80cm away, forming a horizontal interference pattern.
Before starting the experiments, run through the following checklist:
graph of light intensity vs. position. To exit Monitor Mode, click the Stop button at the top of the screen. Clicking the Start button will begin data recording (don't do this yet).
3.3 Recording Data
Move the sensor assembly so that it rests against the black clamp on the Linear Translator rack. Remember to do this before each experiment or the graphs from different experiments will not line up correctly. (DataStudio always defines 0cm to be the location of the sensor assembly when you first pressed the Start button.)
Click the Start button and move the sensor assembly across the entire visible interference pattern. Click Stop when you are finished. If there is a problem during data recording, you can select Delete Last Data Run from the Experiment menu (or press Command-minus), click OK , and start again.
The screenshot above shows a typical DataStudio window with two data sets superimposed: a single-slit data set with a = 0.04mm and a double-slit data set with a = 0.04mm and d = 0.25mm. The icons at the top will be used later for analysis.
Once you are satisfied with your data, repeat the experiment with the following settings. (Use the Double Slit Set accessory for the third and fourth experiments.)
Single Slit: a=0.16mm
Single Slit: a=0.08mm
Double Slit: a = 0.04mm d = 0.25mm
Double Slit: a = 0.04mm d = 0.50mm
3.4 Analyzing Data
The Diffraction and Interference window will show the results of the most recently recorded data. To view all of the data at once, use the Single-Double Comparison window. Click the Data box in the toolbar at the top of the window to select which data recordings should be displayed in the window.
Click the Scale to fit icon at the top left of either window to automatically re-size the displayed data. To zoom in on a particular section of the data, use the Zoom Select icon (a magnifying glass with a + and a dotted rectangle). Click and drag to draw a box and DataStudio will zoom in on that box.
To find the coordinates of an individual data point, click the Smart Tool icon (the letters xy with two perpendicular dashed lines.) Click on the center of the Smart Tool and drag it to a data point to see that point's coordinates.
We are interested in the locations of the local intensity minima of the interference pattern. To find these, drag the Smart Tool to each minimum value. The location will be displayed as an x-coordinate on the graph. Write these down on the data sheet. The Zoom In and Zoom Out tools may be useful for finding minima more precisely.
To keep track of the different minima, we label each with an order number. Minima caused by single-slit diffraction have been labeled m and double-slit interference minima have been labeled n. The different minima are labeled on the data sheet in the order that they appear as the Smart Tool is moved away from the center of the pattern.
Note that DataStudio defines 0cm to be the starting position of the motion sensor, while our theoretical predictions define 0cm as the center of the interference pattern. To correct for this, write down each minimum left of center in the L column and each corresponding mirror-image in the R column. Then calculate the distance ( R - L ) / 2 from each minimum to the midpoint between them.
The single- and double-slit experiments are (hopefully!) unchanged if the sign of y is reversed. Therefore we expect every minimum at y to have a “mirror-image” at - y. If this is indeed a symmetry of the experiment, then the minimum-to-midpoint distances ( R - L ) / 2 should be the same regardless of where we define 0cm to be.
3.5 Evaluating Error
PHYS 201 Pre-Lab 01
Interference and Diffraction Using Visible Light
Name:__________________________ Sec./Group___________ Date:__________
- In this experiment, a red laser will be used instead of a light bulb to demonstrate that visible light can behave like waves. What is the difference between light waves coming from a lightbulb and from a laser, in terms of wave frequency and phase?
- The largest and smallest slits in these experiments are 0.16mm and 0.04mm wide, respectively. The wavelength of the laser light is 650nm. How many wavelengths wide are these slits?
- If one shines a laser with wavelength λ = 650 nm through a single slit of width a = 0.04 mm, draw the diffraction pattern you might expect on a screen 10 m behind slit. How far apart are the minima?
- In the macroscopic world, you know that you can hear but cannot see around corners. Under what conditions does light bend around corners (i.e. diffract)? Explain why sound diffracts easily around a classroom door.
- Suppose you added to the single slit an identical slit a distance d=0.25mm away from the first. Draw the resulting interference pattern you might expect on the same screen. What happens when we increase the distance between slits? What happens in the limit that d becomes arbitrarily large?
PHYS 201 Lab 01 DATA SHEET
Interference and Diffraction Using Visible Light
Name:______________________ Sec./Group_________ Date:__________
Experiment 1: Single Slit a = 0.16mm
m L R (R-L) / 2 Theoretical % error
1 0.325 cm
2 0.650 cm
3 0.975 cm
4 1.300 cm
Experiment 2: Single Slit a = 0.08mm
m L R (R-L) / 2 Theoretical % error
1 0.650 cm
2 1.300 cm
3 1.950 cm
4 2.600 cm
Experiment 3: Double Slit a = 0.04mm d = 0.25mm
n L R (R-L) / 2 Theoretical % error
1 0.104 cm
2 0.312 cm
3 0.520 cm
4 0.728 cm
