1. How thick should a sheet of mica (n = 1.5) be if it is to be as thin as possi

Question

1. How thick should a sheet of mica (n = 1.5) be if it is to be as thin as possible and still give rise to destructive interference for reflection of light in the blue part of the spectrum (use ? = 400 nm)? (The mica is surrounded by air.)

2. Now the mica sits on glass (n = 1.8). How thick should the sheet of mica (n = 1.5) be if it is to be as thin as possible and still give rise to destructive interference for reflection of light in the blue part of the spectrum (use ? = 400 nm)? (All parts of the mica except the bottom surface are still surrounded by air.)

Explanation / Answer

Given data

mica (n = 1.5)

= 400 nm

the thickness of the mica should be equivalent one quarter wavelength of the blue light when travelling through the mica.

The reasoning is that the round trip for the light reflected from the back edge will be 180 degrees out of phase with the incident light and cancel some of the brightness.

The speed of light in the mica is only 1/n times the speed in air. therefore the wavelength is
n times longer

400nm * 1.5 *1/4 = 150nm

2. n=1.8  mica sits on glass

n = 1.5 sheet of mica

= 400 nm

1/2 + 2t/(wavelength/n) = m

2t/(wavelength/n) = 1/2

t = (wavelength/n)/4

t = (wavelength/n)/4

t = (400nm/1.5)4

t = 66.66 nm

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