Physics Lab

Lab 11: Light as a Wave: Interference and Diffraction

Putting a screen with a single slit, or multiple slits, in front of a light source causes that light source to diffract into semicircular waves. The spots where crests of 2 of these light waves meet create bright spots (constructive interference), and the spot where a crest of a light wave meets the trough of a light wave will create a dark spot (destructive interference). Figure 1 below shows what an interference pattern would look like for two slits with light ray interference.

Figure 1: OpenStax Figure 27.1 5 (c)OpenStax College Physics, CC BY

The wave on the right represents the intensity of the light, and the screen behind that shows what the light interference pattern would look like. The bright spots are located where the intensity is highest, and the dark spots are where the intensity is the lowest. The dark spots are called minima and the bright spots are called maxima. The bright spot in the center is the central maxima, and the next maxima above that is the first maxima. The closer the two slits are the more the bright fringes will spread out, and the equation relating these variables is

,

And since sin(Ө) is the ratio of the lengths of the opposite side of the triangle to the hypotenuse,

If the distance between the slit and the screen projecting the interference pattern is very large, then we can use the small angle approximation, and the equation becomes

Single Slit:

1. Open the PhET simulation Wave Interference, and click on the ‘Slits’ option .

2. On the right side of the screen, beneath the Amplitude slider there are three buttons to change the source of the waves (water, sound, and light). Select the light option.

3. Click and drag the measuring tape so it is on the simulation. This is what you will be using to make your measurements.

4. Beneath the source buttons, check the boxes for ‘Screen’ and ‘Intensity’.

5. There is a light yellow line in the middle of your screen. This represents your slit that will diffract light.

6. Using the measuring tape and the green slider beneath the slit, click and drag the sit to be as close to 4000 nm away from the screen as you can get it. Record your actual distance (x) in Table 1.

7. Set the Amplitude of the Light Generator to max and the slit width to 1600 nm using the settings on the right side of the simulation.

8. Turn on the light generator by clicking the green button on the left side. You will see the light rays move through the slit.

9. A few seconds after you turn on the simulation you will see an intensity pattern form both on the screen and to the right on the graph.

10. Using the measuring tape, measure the distance from the central maxima to the first (much lower) maxima. Record this distance in Table 1.

d	x	Y	m	λ
1600 nm			1

Table 1: Single Slit Data

11. This is the only part of the lab where the small angle approximation is not valid (The distance from the screen to the slit is only 4000 nm,or 4 x 10-6 m!). Therefore, we must calculate wavelength (λ) using the full equation. Show your work in the space below. , and solve for λ (m = 1)

12. Calculate the percent error for your wavelength and the wavelength of violet light, 380 nm, showing your work below.

Double Slit:

1. Open The Physics Classroom Interactive Experiment for Double Slits .

2. Note that you can make the window larger by clicking and dragging in the bottom right corner, or you can make it full screen by clicking in the top left corner.

3. Make sure the Slit Width is set to 0.00025 m. If you need to change it, do so by clicking the double slit where it says ‘Tap Me’.

4. Set the screen distance to 4.33 m (x), and the laser to Red Laser.

5. You can see the pattern created by the laser and double slit below the simulation. The bright spot at the 10 cm mark is the central maxima.

6. Measure the distance between the central maxima and the first two maxima using the ruler below the light spots. Each line stands for 1 cm. Record your distances in the table below in METERS.

7. Repeat steps 5 and 6 for slit widths of 0.0003 m, 0.0004 m, and 0.005 m.

Grating	Y (m = 1)	Y (m = 2)	λ (m = 1)	λ (m = 2)	Average λ
0.00025 m
0.0003 m
0.0004 m
0.0005 m
Average Wavelength (λ)

Table 2: Double Slit Data

8. In order to calculat wavelength, we can use the small angle approximation. , and solve for λ. Show your work for one calculation in the space below:

9. Calculate the percent error for your average wavelength and the wavelength of red light, 700 nm, showing your work below.

Diffraction Grating:

1. Open the oPhysics: Interactive Physics Simulation Diffraction Grating Laser Lab

2. Right away, you will see a ruler. If you scroll down you will see the simulation with the laser and diffraction grating off to the side. Notice that the laser is hitting the screen unperturbed.

3. Scroll back up and set the screen to grating distance (x) to 10 m, the Grating lines per mm to 500 mm, and the wavelength to 400 nm.

4. Check the box to put the diffraction grating in place.

5. If you look at the simulation again you will see the laser is now being diffracted and split into multiple rays before striking the screen. The ruler shows the dots that represent the maxima. The dot at 0 represents the central maximum. Record the distance from the central maximum to the first 2 maxima to the right of the central in the table below. Repeat steps 3 and 4 for Grating lines per mm of 400 and 500, keeping the Screen Distance and wavelength constant.

Grating (lines/mm)	Grating (mm/line)	Y (m = 1)	Y (m = 2)	λ (m = 1)	λ (m = 2)	Average λ
500
400
300
200
Average Wavelength (λ)

Table 3: Diffraction Grating Data

6. In order to calculate wavelength (λ), we can use the same equation as the one above for the double slit. In the case of the diffraction grating, d is the distance between consecutive slits, which can be calculated as (1/Grating lines per mm), then we can calculate wavelength using . Show your work for one calculation in the space below.

7. Calculate the percent error for your average wavelength and the wavelength given in the simulation, showing your work below. Post-Lab Problems from OpenStax College Physics, CCBY : (show your work)

1. Suppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of 10.95º relative to the incident beam. What is the wavelength of the light?

2. Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on double slits separated by 0.100 mm.

3. Find the distance between two slits that produces the first minimum for 410-nm violet light at an angle of 45.0º

4. At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?