suppose you have a HeNe laser shooting photons at a surface, composed of two fil

Question

suppose you have a HeNe laser shooting photons at a surface, composed of two films. film 1 has an index of refraction of 1.3000 and film 2 has an index of refraction of 1.1005. if you want all three reflected rays to combine to produce the brightest possible refraction, how thick should the two films be?

Note: This problem can be extended to an infinite

number of layers. When you minimize the time that

light takes to travel through the entire material the

path it takes is a cycloid. This general problem is

referred to as the Brachristochrone problem.!

Explanation / Answer

The best known and most widely used HeNe laser operates at a wavelength of 632.8 nm.

2 n1 t1 = lambda

==> t1 = lambda/(2 n1) = 632.8/(2*1.3000) = 243.38 nm

thikness of the film1 = t1 = 243.38 nm

2 n2 t2 = lambda

==> t2 = lambda/(2 n2) = 632.8/(2*1.1005) = 287.51 nm

thikness of the film2 = t2 = 287.51 nm

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