Young's Double-Slit Experiment
Objective:
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 (The built-in calculator of the computer may be used), 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 go to maximum and minimum together are called coherent waves. Coherent waves help each other’s effect, add constructively, and cause constructive interference. They form a bright fringe.
Destructive Interference of Waves
In Fig. 2 however, the situation is different. When wave with amplitude A_{1} is at its maximum, 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 sin(θ_{k}) = k λ where k = 0,1,2,3, ...
Dark Fringes: d sin(θ_{k}) = (k + 1/2) λ where k = 0,1,2,3, ...
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 3(½ λ) out of phase (same as being ½ λ out of phase) and therefore form a dark fringe.
Light rays going to B_{1} from S_{1} and S_{2} are 2(½ λ) out of phase (same as being in phase) and therefore form a bright fringe.
Note that SB_{o} is the centerline.
Going from a dark or bright fringe to its next fringe changes the distance difference by ½ λ.
Diffraction Grating: (This experiment is not based on Diffraction Grating and you may skip this part)
Diffraction grating is a thin film of clear glass or plastic that has a large number of lines per (mm) drawn on it. A typical grating with a poor line density is (250 lines)/mm. Using more expensive laser techniques, it is possible to create line densities of (3000 lines)/mm or higher. When light from a bright and small source passes through a diffraction grating, it generates a large number of sources. The very thin space between every two adjacent lines of the grating becomes an independent source. These sources are coherent sources meaning that they emit in phase waves with the same wavelength. These sources act independently such that each source sends out waves in all directions. On a screen a distance (D) away, points can be found whose distance differences from these sources are different multiples of λ causing bright fringes. One difference between the interference of many slits (diffraction grating) and double-slit (Young’s Experiment) is that the former makes principle maximums with smaller intensity maximums in between. The principal maximums (Maxima) occur on both sides of the central maximum at points (or angles) for which a formula similar to Young’s holds true.
D = the distance from the grating to the screen.
d = the spacing between every two lines (same thing as every two sources)
If there are (N) lines per mm of the grating, then (d), the space between every two adjacent lines or (every two adjacent sources) is
The diffraction grating formula for the principal maxima is:
d sin ( θ_{k}) = k λ where k = 1, 2, 3, ...
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 slider for the "Angle" 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 sin ( θ_{k}) = k λ. This calculated value will be the accepted value. In each case, calculate a % error on θ_{1} only.
Part 1:
As a start, set the wavelength at λ = 656nm ( Red) and d = 3600 n m, slits separation. (This means that d = 0.0036 m m, a very small separation between the slits)
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.
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 wavelength has on the number of fringes.
Discussion:
To be explained by students