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

Question

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 lambda = 404 nm)? (The mica is surrounded by air.) thickness = 134.6 nm. 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 lambda = 404 nm)? (All parts of the mica except the bottom surface are still surrounded by air.) thickness = 134.6 nm

Explanation / Answer

(a) Destructive interference due to reflection occur when:

m = 2nt                 m = 0,1,2,3,····

t is minimum when m = 1, so eqn is

tmin = / 2n

tmin = 404 * 10^-9/ 2*1.5

tmin = 1.35 * 10^-7 m

tmin = 135 nm

(b)       tmin = / 4n

tmin = 404 * 10^-9/ 4*1.5

tmin = 6.73 * 10^-8 m

tmin = 67.3 nm

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