a) How thick should the coating of a material with index of refraction 1.42 on a

Question

a) How thick should the coating of a material with index of refraction 1.42 on a piece of flat transparent material of index of refraction 1.57 if we wish that there is no reflection for light of wavelength 642 nm? Provide your answer in nm.

b) How thick should the coating of a material if we wish that there is maximum transmission for light of wavelength 642 nm? Provide your answer in nm.

c) What if we want to place the coating over a transparent material of index of refraction 1.18 and we wish that there is maximum transmission for light of wavelength 642 nm, what should the thickness of the coating be? Provide your answer in nm.

Explanation / Answer

Part A)

The formula to apply in this case is 2nt = (m + .5)(wavelength)

2(1.42)(t) = (.5)(642 X 10-9)

t = 113 nm

Part B)

Maximum transmission means the same thing no reflection. Thus this is the same exact solution as part A

t = 113 nm

Part C)

In this case, 2nt = m(wavelength)

2(1.42)(t) = (1)(642 X 10-9)

t = 226 nm

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