Question

A sheet of glass (n=1.50) is coated with a 500 nm -thick layer of oil (n=1.42).

A. For what visible wavelengths of light do the reflected waves interfere constructively? The range of wavelength of visible light is from 380 nm to 750 nm.

B. For what visible wavelengths of light do the reflected waves interfere destructively?

C. What is the color of reflected light?

D. What is the color of transmitted light?

Answer 1

(a) We know that for constructive interference of the reflected waves, the path difference must be a whole number of wavelength.

2t = m / n_oil

= 2tn_oil / m

start from m = 1

= 2 * 500 * 1.42 = 1420 nm ( not possible - out of visible range)

= 2 * 500 * 1.42 / 2 = 710 nm ( not possible - out of visible range)

= 2 * 500 * 1.42 / 3 = 473 nm ( possible - within the visible range)

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(b) for destructive interference of the reflected waves, the path difference should be a half-integer multiple of the wavelength.

= 2tn_oil / m + 1/2

for destructive, start from m = 0

= 406 nm ( for m = 3)

= 568 nm ( for m = 2)

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(c) color of reflected light is Blue ( 473 nm )

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(d) color of transmitted light is violet (406 nm) and green ( 568 nm) .