Question

A thin film of acetone (n = 1.25) coats a thick glass plate (n=1.50). White light is incident normal to the film. In the reflections, fully destructive interference occurs at 600 nm and fully constructive interference at 675 nm. Calculate the thickness of the acetone film.

Answer 1

the incident light is in a low index medium, the thin film of acetone has somewhat higher n = n2, and the last layer (the glass plate) has the highest refractive index. To see very little or no reflection, according to the condition,

2L = (m + 0.5)*lambda/n2, where m = 0,1,2,.........

must hold.

with n2 = 1.25 and lambda = 675 nm yields

L = 0, 270nm, 540nm, 810nm,1080nm.....

for the first several m values. And the equation shown above  gives, with lambda = 600 nm,

L = 120nm, 360nm, 600nm, 840nm,1080nm,....

for the first several m values. The lowest number these lists have in common is L = 1080 nm