Antireflection coatings can be used on the inner surfaces of eyeglasses to reduce the reflection of stray light into the eye, th

Question

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Antireflection coatings can be used on the inner surfaces of eyeglasses to reduce the reflection of stray light into the eye, th

us reducing eyestrain.PART A) 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. n = _____ .PART B) 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 ? The thinnest possible coating is best.t = _____ nm .

Physics

1 answer:

Maru [3.3K] · Answer 1 · 2026-03-10T09:36:12+03:00

Answer:

a) n = 1.33, b) t = 87 10⁻⁹ m

Explanation:

In Part A.

The very thin anti-reflection layer needs to induce destructive interference for the targeted wavelength.

2t sin θ = (m + ½) λₙ

The factor of 2 comes from the path of light inside the film, where λₙ is the wavelength adjusted for the film's refractive index

λₙ = λ₀ / n

2t = (m + ½) λ₀ / n

n = (m+ ½) λ₀/2t

Assuming we are evaluating the first interference order, where m = 0

n = (½ 480 10-9)/ 2 90

n = 1.33

In Part B

We may not have the exact refractive index for the glass, but it generally approximates around 1.5; since the film's index is less, it incurs no phase alteration.

2t = (m + ½) λ₀ / n

t = 1/4 480 10⁻⁹ / 1.38

t = 87 10⁻⁹ m