VL 10 – Interference and Diffraction Last week we finished the second lab using the ray model of light or geometrical optics. This week’s lab examines the wave nature of light in detail. Refer to Chapter 17 of your textbook if you need to remind yourself of any concepts.
1) Waves including light and sound exhibit interference which is an effect of two or more waves being superimposed or added at the same location and time. This can be constructive such that the intensities of both wave combine to yield a higher intensity than each can produce independently or it can be completely destructive so no intensity is observed. (Of course anything in between these two extremes can also occur 😉
a) Draw a diagram of two slits, each of width “a”, separated by a distance “d” and a screen “x” away from the plane of the slits. Pick a point on the screen above the higher slit and indicate the paths that two light waves would travel if one is coming from the center of the top slit “r1” and the other from the center of the bottom slit “r2”.
b) Without deriving anything just indicate on your diagram what the path length difference “∆r” is for the two waves you indicated previously. Now express “∆r” in terms of “r1” and “r2”.
c) Finally express “∆r” in terms of the wavelength of light used to illuminate these two slits for the two conditions of completely constructive and destructive interference.
d) Using your text draw an intensity vs. position plot of a two slit interference pattern and label the bright fringes according to the formula given in your text and lab manual for “y”. Include the formulas for the locations of the interference minima and maxima.
2) Please navigate to the “Interference” PHET here: https://phet.colorado.edu/en/simulations/wave-interference Explore with the water spigot point source, then the sound waves coming from two speakers and finally with the lasers.
a) Click on the “graph” and “intensity”. What is the biggest difference you see between the interference pattern shown on the screen from the red and violet light sources.
b) What effect does changing the distance between the two sources for maximum to minimum values have? Describe below.
c) Lastly vary the amplitude. What occurs when the amplitude is dialed down? Why do you think this occurs?
3) Diffraction is more difficult to explain than interference. I like to call it “self interference”. Indeed as it is as though the wavelets postulated by Huygens principle are all acting as individual waves which then interfere with each other to produce a pattern of varying intensity similar to an interference pattern. The essential difference being that this occurs with only one slit! Find the diagram of the intensity vs. screen position for single slit diffraction in your text and reproduce it here. Include the formula for the diffraction intensity minima.
4) Please navigate to the “Slits” PHET here: https://phet.colorado.edu/en/simulations/wave-interference Explore with the water spigot point source, then the sound waves coming from two speakers and finally with the lasers.
a) Click on the “graph” and “intensity”. What is the biggest difference you see between the diffraction pattern shown on the screen from the red and violet light sources.
b) How does varying the slit width affect the diffraction pattern?
c) Now click to “two slits” and you will see the familiar interference pattern.
5) In which pattern, interference or diffraction, are the minima or dark fringes spaced further apart? Using this information draw a qualitative graph of what the intensity pattern of real two slit interference might look like if both interference and diffraction are evident.
As illustrated in VL 8 Reflection and Refraction, dispersion describes the property of light by which a prism is able to separate the colors of white light into a rainbow or spectrum (ROYGBIV). This occurs because the refractive index of light depends on its frequency, so different colors travel at different velocities in a medium. In order for all the different colors of the spectrum to exit the prism at the same time, the frequency traveling at a slower speed will need to take a shorter path than a frequency traveling at a faster speed through the same medium.
6) Diffraction can also separate white light into its constituent frequencies. This is based solely on the idea of diffraction being a self interference phenomenon. Completely constructive interference occurs for waves when the path length difference for two waves (or wavelets in the case of diffraction) is equal to an integer number of wavelengths. Since different colors have different wavelengths the locations of these maxima will be different. This phenomenon is exploited in a diffraction grating spectrometer. A diffraction grating consists of a very large number of fine slits which yields very sharp interference maxima preventing one frequency from overlapping with another.
a) Which color, Red or Violet, will have a first order bright fringe closer to the central maximum?
b) Draw a qualitative diagram of the spectrum you would expect from the dispersion of white light by the diffraction grating below.
If an image is made through a small aperture, there is a point at which the resolution of the image is limited by the aperture diffraction. As a matter of general practice in photographic optics, the use of a smaller aperture (larger f-number) will give greater depth of field and a generally sharper image. But if the aperture is made too small, the effects of the diffraction will be large enough to begin to reduce that sharpness, and you have reached the point of diffraction-limited imaging.
7) Please navigate to the “Diffraction” PHET here: https://phet.colorado.edu/en/simulations/wave-interference Explore diffraction with the various apertures available. What light frequency gives the clearest ie least fuzzy image? (Red or Violet)
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