Antireflection coatings can be used on the inner surfaces of eyeglasses to reduc

Question

Antireflection coatings can be used on the inner surfaces of eyeglasses to reduce the reflection of stray light into the eye, thus reducing eyestrain. A 90 nm- thick coating is applied to the lens. What must be the coating's index of refraction to be most effective at 480 nm? (Assume that the coating's index of refraction is less than that of the lens) If the index of refraction of the coating is 1.38, what thickness should the coating be so as to be most effective at 480 nm? (the thinnest possible coating is best)

Explanation / Answer

Because N(air)<N(film)<N(glass), both of these reflections introduce an equal phase shift (lambda/2), the two-way trip through the film should cover a distance of lambda/2 to provide a net lambda/2 phase difference. So the film should be lambda/4 thick.
Wavelength within the film = 480/N nm.
a)

Thus we want (480/N)/4 = 90 ==> N = (480/4)/90 = 1.33

B)

If N = 1.38, we want thickness T = (480/1.38)/4 = 86.95 nm

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