Question

Consider a glass block (n=1.5) that is covered by a thin transparent film (n=1.25). White light is incident normal to the film. When viewed in reflected light, fully destructive interference occurs at 600 nm and fully constructive interference at 700 nm.

A) Calculate the thickness of the film.

B) How much light (%) will pass through the film into the glass?

Answer 1

A)

_d = wavelength for destructive interference = 600 x 10^-9 m

_c = wavelength for constructive interference = 700 x 10^-9 m

m₂ = order for constructive interference = ?

m₁ = order for destructive interference = ?

n = index of refraction of film = 1.25

t = thickness

for destructive interference :

2nt = (m₁ + 0.5) _d eq-1

for constructive interference

2nt = (m₂ ) _c eq-2

using eq-1 and eq-2

(m₁ + 0.5) _d = (m₂ ) _c   

(m₁ + 0.5) (600) = (m₂ ) (700)

(m₁ + 0.5)/m₂ = 7/6

(2 m₁ + 1)/m₂ = 14/6

(2 m₁ + 1)/m₂ = 7/3

m₂ = 3

m₁ = 3

using eq-1

2nt = (m₁ + 0.5) _d  

2(1.25)t = (3 + 0.5) (600)

t = 840 x 10^-9 m