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Theory
Theory
Interference
Interference
Interference is a process in which multiple waves combine to produce a resultant wave, which is the sum of the amplitudes of the various waves. If the waves are in phase (the same frequency and the maxima happen at exactly the same time), at some points an interference may be observed (see the figure below). In case (a), crests and troughs add creating a wave of a double amplitude. It is called a constructive interference. In case (b), crests and troughs cancel each other creating spots/patterns of no amplitude. It is called a destructive interference.
Figure 1. Constructive (a) and destructive (b) interference
Diffraction
Diffraction
Diffraction is the process by which a beam of light spreads out or the edge rays deflect away from the center of a beam. That can be explained with the Huygens's principle, which states that every point on a wave may be considered a source of spherical wave. Specifically, if the edge point of a wave passing through an opening becomes a source of a new wave, it can propagate in any direction, not only straight ahead. Hence, we observe deflection of light at the edge.
Fig 2. Diffraction
That is the reason that, if you observe a shadow, it does not have sharp edges - the rays on the edge of the object deflect slightly. It seems like the rays of light go around corners (see Figure 3).
Figure 3. The shadow during Solar eclipse (source)
Diffraction & Interference
Diffraction & Interference
Many physicists confuse diffraction with interference, and here is how: Because all the points of the same wave are in phase, the new spherical waves created according to the Huygens's principle interfere creating higher amplitude at some points or no amplitude at some points (Figure 4a, see the two points of purple waves). If the interference patterns of light can be observed on a screen, they form a set of bright and dark fringes.
Figure 4a. Two waves generated by points "in phase" interfere
Figure 4b. Bright and dark fringes observed on a screen.
For the first time, both phenomena were observed by Thomas Young in 1803 (1:30, Video 1 below).
This short video is a good introduction to the Interference and diffraction experiment whose effects can be explained only by assuming the wave nature of light. Notice people's reactions to what they see. Indeed, the results are counterintuitive for those who have not studied physics.
In Video 2, an interesting phenomenon of a light spot in the center of a shadow is explained. This is one of the lesser-known examples of phenomena that demonstrate the wave nature of light.
Video 1
Video 2
Summary
Summary
The key information is the set of light and dark spots created by constructive and destructive interference, respectively.
Experimental Procedure
Experimental Procedure
Experimental Settings
Experimental Settings
Set the laser, diffraction grating, and the screen as shown in the picture (Figure 5)
Figure 5
Part A. Measurements
Part A. Measurements
Measure the distance between two light fringes (two maxima) in a diffraction grating experiment.
Calculate slits spacing d in the diffraction grating (Figure 7)
Select a laser (red, blue, or green).
Measure y (Figure 6).
Measure L (Figure 6).
Collect your data in the Data Collection Table (Figure 8).
Repeat Part A and Part B of the Quantitative Experiment for at least five different wavelengths and slit spacing.
Figure 6
Figure 7. Diffraction grating
Figure 8. Data Collection Table
Part B. Calculations
Part B. Calculations
Calculate the distance between two light fringes (two maxima) in the experiment for the same setting as above. Use the formula derived below (the formula in red).
Compare the results (find the percent difference).
Diffraction Grating Formula
Diffraction Grating Formula
Video 3
As explained in the video, the diffraction grating formula is
n λ = d sin(θ)
where n is the order of maximum, lambda is the wavelength, d is the distance between slits in the diffraction grating, and theta is the angle of diffraction. If we approximate sine theta with the y/L ratio (y is the distance between the nth maximum and the central one, L is the distance between the diffraction grating and the screen; see Figure 10)*, the formula is
n λ = d y/L
To calculate y:
y = n λ L/d
(*) You may be wondering how come that sine theta was approximated with y/L, while this is actually the tangent of theta.
Graphs of those two functions should help you see that, especially for small angles, the sine and tangent of an angle have similar values. In Figure 11, the red graph represents sine while the blue one represents the tangent function.
For angles between -10 and 10 degrees, the lines are indistinguishable. The numerical values of sine and tangent differ only in the third decimal place:
sin θ = 0.1736
tan θ = 0.1763
Given the measurement error, the difference may be neglectable.
Figure 9. Sine and Tangent for Small Angles (here is a link to Desmos)
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