Question

A soap film (n=1.33) is 785 nm thick. White light strikes the film at normal incidence. What visible wavelengths will be constructively reflected if the film is surrounded by air on both sides? If there is more than one answer, separate them by a comma.

Answer 1

For constructive interference, the formula to apply is

2nt = (m + .5)λ

λ =2nt / (m + .5)

this is trial and error question  

try with m = 0 so

2*1.33*785 =0.5λ

λ = 2*1.33*785/0.5 =4176.2 nm not in visible range

try with m = 1 so

λ = 2*1.33*785/1.5 =1392.06667 nm not in visible range  

try with m = 2 so

λ = 2*1.33*785/2.5 =835.24 nm not in visible range  

try with m =3 so

λ = 2*1.33*785/3.5 =596.6 nm in visible range  

try with m =4 so

λ = 2*1.33*785/4.5 =464.022222   nm in visible range  

try with m =5 so

λ = 2*1.33*785/5.5 =379.654545   nm not in visible range  

so answer are in bold

596.6 nm , 464.022222   nm  

Goodluck for exam Comment in case any doubt, will reply for sure..