A thin film of oil noil 136 is on a glass slide nglass 170

A thin film of oil (noil = 1.36) is on a glass slide (nglass = 1.70). When light of many wavelengths is incident on the film at near-normal incidence, it is observed that light of wavelength ? = 579 nm (in vacuum) is strongly transmitted into the glass, i.e. not reflected back into the air. What is the smallest thickness that this film of oil can have?

WARNING, NO ONE HAS BEEN ABLE TO GET THIS QUESTION CORRECT. (BOTH 62.60nm AND 209.78nm ARE INCORRECT ANSWERS)

Solution

condition for destructive interference

path difference = m+1/2)*(lemda)

2t = m+1/2)*(lemda)

tmin = (0+1/2)*(lemda/2)

=> lemda1 = lemda/(n0*ng)

= 579/(1.36*1.70) = 250.43 nm

tmin = (1/2*lemda1)/2 =   250.43/4 = 62.60 nm