Question

A soap film of thikness 0.0011 mm appears dark when seen by the reflated light of wavelength 580 nm. What is the index of refraction of the soap solution, if it is known to be between 1.2 and 1.5 ?

Answer 1

For destructive interference-

Path length=$\Delta x=2\mu t=\left(n\right)\lambda$

$⟹\mu =\left(n\right)\frac{\lambda }{2t}=\left(n\right)\frac{580\times {10}^{-9}}{2\times 11\times {10}^{-7}}$

$⟹\mu =\left(n\right)\times 0.263$

Hence, $\mu =1.315$ for $n=5$