Young's Double-Slit Experiment
Objective:
The objective is to verify the wave nature of light by forming the interference patterns in a Young's Double-Slit Experiment and measuring the angles corresponding to the formed fringes.
Equipment:
A computer with the Internet connection, a calculator, a few sheets of paper, and a pencil
Theory:
Young's Double-Slit Experiment verifies that light is a wave simply because of the bright and dark fringes that appear on a screen. It is the constructive and destructive interference of light waves that cause such fringes.
Constructive Interference of Waves
The following two waves (Fig. 1) that have the same wavelength and are in phase as well are called "coherent." Coherent waves help each other's effect, and cause constructive interference.
Destructive Interference of Waves
In Fig. 2, the situation is different. When the wave with amplitude A_{1} is at its maximum, the wave with amplitude A_{2} is at its minimum and they work against each other resulting in a wave with amplitude A_{2} - A_{1}. These two completely out of phase waves interfere destructively. If A_{2} = A_{1}, they form a dark fringe.
The bright and dark fringes in the Young's experiment follow the following formulas:
Bright Fringes: d sinθ_{k} = k λ where k = 0, 1, 2, 3, ...
Dark Fringes: d sinθ_{k } = (k - 1/2 )λ where k = 1, 2, 3, ...
The above formulas are based on the following figures:
Check the following statements for correctness based on the above figure:
Light rays going to D_{2} from S_{1} and S_{2} are 3λ/2; out of phase (same as being λ/2 out of phase) and they form a dark fringe.
Light rays going to B_{1} from S_{1} and S_{2} are 2λ/2 out of phase (same as being in phase) and they form a bright fringe.
Note that SB_{o} is the centerline.
Going from a dark to the next bright and vice versa changes the distance difference by λ/2.
Procedure:
Click on the following link: http://www.walter-fendt.de/ph14e/doubleslit.htm
On this applet, there are 3 horizontal sliders that you can slide with the mouse to change and read the following variables:
1) The wavelength, λ
2) the slits separation, d, and
3) the fringe angle, θ.
There are two other options of "interference Pattern" and "intensity Profile." Try both to see what each means. While you run the experiment, let the applet be on the "interference Pattern" option.
Run the applet for the cases shown in Table 1. In each case, the values of λ and d are given. Set the applet on these values. θ_{k} can be measured by moving the "Angle" slider and observing the two downward arrows on the applet move. As you move the slider with the mouse, the downward arrows move and you can adjust them exactly at the center of each fringe and read its corresponding angle from the box on the top of the slider. This will be your measured value for θ_{k }.
You can also calculate θ_{k} from the formula: d sinθ_{k} = k λ . This calculated value will be the accepted value. In each case, calculate a % error on θ_{1} only.
Part 1:
1) As a start, set the wavelength at λ = 656nm (Red) and d = 3600 nm, the slits separation. (This means that d = 0.0036 mm, a very small separation between the slits)
2) You should get 5 fringes on each side of the central fringe. Check the approximate angles and see if you get them about the following values: 11, 22, 33, 47, and 66 degrees. Try to adjust the slider position to best of your judgment and record the angles to one decimal place. For each of these measured angles, you need to calculate a corresponding accepted value from the formula and record it in the space provided. Note that in each trial, the accepted value or the calculated value must be recorded under its corresponding measured value in Table 1.
3) Proceed to complete Table 1.
Part 2:
For each case of Part 1, change d with the slider and see how the number of fringes changes. Make sure that you give an explanation to this effect under your conclusion. Also, in each case of Part 1, change the wavelength to see its effect on the number of fringes. As far as measurement and calculations are concerned, Table 1 will be sufficient.
Data:
Part 1: Given and Measured:
Trial | λ (nm) | Slits Gap d (nm) | Meas. θ_{1} | Meas. θ_{2} | Meas. θ_{3} | Meas. θ_{4} | Meas. θ_{5} | % error on θ_{1} | |
Accpt. θ_{1} | Accpt. θ_{2} | Accpt. θ_{3} | Accpt. θ_{4} | Accpt. θ_{5} | |||||
1 | 656 Red | 3600 | |||||||
2 | 489 Green | 2000 | |||||||
3 | 410 Violet | 2000 | |||||||
Part 2: To be explained under "Conclusion."
Calculations:
To be performed by students
Comparison of the Results:
To be completed by students
Conclusion:
To be explained by students. Make sure that you explain how the slits separation affects the number of fringes. You may also explain about the effect that wavelength has on the number of fringes.
Discussion:
To be explained by students