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 l = 428 nm)? (The mica is surrounded by air.)

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 l = 428 nm)? (All parts of the mica except the bottom surface are still surrounded by air.)

Explanation / Answer

The refractive index of mica is n = 1.5 The wavelength of the light used is = 428 nm The condition for the destructive interference due to thin film is 2t = m For the least possible thickness, m = 1 2t = 2*1.5*t = 428 nm t = 142.67 nm If the film sits on glass of rfractive index n' = 1.8 The condition for the destructive interference due to thin film is 2t = (m+1/2) For the least possible thickness, m = 0 2t = /2 2*1.5*t = 214 nm t = 71.33 nm If the film sits on glass of rfractive index n' = 1.8 The condition for the destructive interference due to thin film is 2t = (m+1/2) For the least possible thickness, m = 0 2t = /2 2*1.5*t = 214 nm t = 71.33 nm The condition for the destructive interference due to thin film is 2t = (m+1/2) For the least possible thickness, m = 0 2t = /2 2*1.5*t = 214 nm t = 71.33 nm

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