Question

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

Answer 1

the required minimum thickness is 179.19 nm

Step-by-step 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
`_{min` will be;

L
`_{min` = 1 × ( 179.19 nm )

L
`_{min` = 179.19 nm

Therefore, the required minimum thickness is 179.19 nm