While reading about double slit experiment I have found no article where the amplitudes of light at the board ( on which light falls) is calculated . Only the fringe width and intensity ratios are found . Can anyone guide me how to find the amplitudes because it will give me more insight into nature and propagation of light?
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$\begingroup$ if it helps .... all light that passes thru slits makes it to the screen. Bright bands have all the light, dark bands none. The EM field guides all the photons. $\endgroup$– PhysicsDaveCommented May 19 at 22:34
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$\begingroup$ Diffraction in two-slit experiments is often treated as a boundary value problem. You prescribe the intensity of light at the screen (no-light, light, no-light) and then calculate how it will diffract. Actually calculating the diffraction of a plane wave on a screen will require specifying what material the screen is made of: dielectric, metal etc. you will also need to worry about the thickness of the screen, perhaps even the sharpness of the edges. All interesting problems, but somewhat irrelevant for diffraction. $\endgroup$– CryoCommented May 20 at 8:50
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$\begingroup$ Usually those sort of problems are studied as part of more general electromagnetism, in the context of EM propagation between different domains. $\endgroup$– CryoCommented May 20 at 8:51
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$\begingroup$ EM book has already been recommended, I would add en.wikipedia.org/wiki/Principles_of_Optics for optics specifically . Chapter 8 is on diffraction, chapter 10 is on rigorous diffraction $\endgroup$– CryoCommented May 20 at 8:55
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2 Answers
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In microwave engineering (which will give the same calculation in classical optics) the light intensity is calculated in the far field from electric and "effective" magnetic current on the slits. There is a book [Smolders, Visser, Johansen "Modern Antennas and Microwave circuits", 2020], see the chapters on the far field and horn antennas. It could be found on Coursera or just on web.
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The amplitude is the square root of the intensity. Which square root? Well, for the double slit experiment you may consider that the bright bands' amplitudes alternate in sign. Positive or negative depends on your phase convention: your choice.
More complicated diffraction problems require a more sophisticated approach to phase.
