[Solution]Interference in Young’s Interferometer

In this lab, you will explore interference effects in a Young’s interferometer. You will use a simulation to measure interference effects and use the measured…

In this lab, you will explore interference effects in a Young’s interferometer. You will use a simulation to measure interference effects and use the measured position of interference fringes to determine the wavelength of the incident light—a primitive form of spectroscopy.
The basic equation you will explore is that of constructive interference:
 
. (1)
In this equation, d is the spacing between the slits, θ is the angle of propagation of the interference fringe, m is the order of the fringe, and λ is the wavelength.
If we solve for the sine of the angle and set m = 1, we get the following equation:
(2) If we plot the inverse of the slit spacing on the horizontal axis and the sine of the angle on the vertical axis, the slope will be the wavelength of the light.
You will determine the angle of the first order maximum for a range of slit spacings d, then analyze the graph to determine the wavelength. You will do this for several different colors of light, thus determining the wavelength of the different colors.
OBJECTIVES
In this experiment, you will
 Measure the interference angle to the first order maximum for several different colors and spacings of slits.
 Use this data to determine the wavelengths of the different colors.
PROCEDURE 1
Go to this website.
https://phet.colorado.edu/sims/html/wave-interference/latest/wave-interference_en.html
and click on the “Slits”
You should see the following:
To begin, click on the laser symbol on control panel, and choose two slits. Then move the screen with the slits as close as possible to the light generator. Change slit width to minimum value and turn on light generator with the button on left. Finally, click on screen and intensity in control panel.
 
You should then see what is shown below:
 

Now you are able to follow the procedure below. You will repeat this procedure for several different colors. Your instructor will tell you which colors and how many.
BASIC PROTOCOL
Record all data in Excel or LoggerPro.
Before you start measure the horizontal distance (using tape measure) from the screen with the slits to the screen where the fringes are projected. Call this L. This will be the same for all data sets. You will need this for calculating the angle.
1. Move slit separation to minimum value (as close as possible) and you are still able to see the first order (m=1) fringe. As d decreases, the m=1 fringe will move up, stop before it moves out of the range of view.
2. Wait for the pattern to stabilize and then use the tape measure to measure the distance in the projection screen from the center of the forward (m=0) bright fringe to the center of the m=1 bright fringe. The is Δy.
3. Record the slit separation and the Δy value in a table.
4. Now repeat this same procedure, but move the slit separation to slightly larger, by about 200 nm. You will repeat the Δy measurement as before, and record the new d and Δy values in your table.
5. Continue until you have at least 8 data points in your table.
Once you have this data set, you will change the color of the laser light and repeat the process to collect a new data set for this new color. Keep repeating the process, each time for a new color, until you have as many data sets as your instructor tells you.
ANALYSIS OF DATA
You will perform this analysis for each data set.
1. First you must calculate the sine of the angle of the interference fringe from your measurements of Δy and L. Create a new column for the sine of angle using the following formula (do you see why this is the sine?).
2. Transform the slit spacing data d to create a new column that is 1/d.
3. Insert a graph of sin(θ) on the vertical axis and 1/d on the horizontal, and add a trend line.
4. Now find slope and the intercept. Using equation (2), you can see that slope of the graph is the experimental value of wavelength.
5. Find percent error between experimental value of wavelength and standard value of wavelength (given below).
STANDARD VALUES OF WAVELENGTHS:
 
· Violet: 380–450 nm (688–789 THz frequency)
· Indigo: 445 – 464 nm
· Blue: 450–495 nm
· Green: 495–570 nm
· Yellow: 570–590 nm
· Orange: 590–620 nm
· Red: 620–750 nm (400–484 THz frequency)

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