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

Question

Antireflection coatings can be used in the inner surfaces of eyeglasses to reduce the reflection of stray light Into the eye, reducing eyestrain. a A 50-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 coatings index of refraction is less than that of the lens, b. If the index of refraction of the coating is 1.38, what thickness should be the coating be as to be most effective at 480 nm? The thinnest possible is best.

Explanation / Answer

Assuming the stray light of concern comes from the rear, it hits the film first, and part reflects back and the rest travels through the film to the glass, where another part reflects back. The idea is to have the two back-reflections out of phase (i.e., having a lambda/2 phase difference) for a minimum total reflection. 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.
Thus we want (480/N)/4 = 90 ==> N = (480/4) / 90 = 1.33 (answer A)
If N = 1.38, we want thickness T = (480/1.38)/4 = 86.95 nm (answer B)

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