Question

White light is incident on a soap film of refractive index $\frac{4}{3}$ at an angle of reflected light is observed to have a dark band for wavelength $6\times {10}^{-5}$ cm. Calculate the minimum thickness of the film.

Answer 1

For dark band, there should be destructive interference.

Path difference$=\Delta x=2\mu t=(n+\frac{1}{2})\lambda$

For minimum thickness, $n=0$

$⟹2\mu t=\frac{\lambda }{2}$

$⟹t=\frac{\lambda }{4\mu }$

$⟹t=\frac{6\times {10}^{-7}}{4\times \frac{4}{3}}$

$⟹t=1.125\times {10}^{-7}m$