A sheet of glass having an index of refraction of 1.49 is to be coated with a film of material having an index of refraction of 1.62 in order that green light with a wavelength of 534 nm (in air) will be preferentially transmitted via constructive interference. (a) What is the minimum thickness of the film that will achieve the result

the required minimum thickness is 179.19 nm

Explanation:

Given the data in the question;

Refraction index of air n₁ = 1

Refraction index of sheet n₂ = 1.49

Refraction index of film n₃ = 1.62

wavelength of green light λ = 534 nm

In the data given, n₂ > n₃

so, this case has no pie-phase shift,

the condition for constructive interference will be;

mλ = 2Ln₂

L = mλ / 2n₂

so we substitute

L = m(534) / 2( 1.49 )

L = m( 534/ 2.98 )

L = m( 179.19 nm )

so for minimum value of L,

let m = 1

such that, L will be;

L = 1 × ( 179.19 nm )

L = 179.19 nm

Therefore, the required minimum thickness is 179.19 nm

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