A parallel beam of white light falls on a thin film whose refractive index is 1.33. If angle of incidence is 52° then thickness of the film for the reflected light to be coloured yellow (λ = 6000 Å) most intensively must be

$0.14 (2n + 1) μm$

$μ=\frac{\sin i}{\sin r}⇒\sin r=\frac{\sin i}{μ}=\frac{0.788}{1.33}=0.6$

$\cos r=\sqrt{1-\sin^2r}=\sqrt{1-(0.6)^2}=0.8$

For constructive interference on reflection

$2μt\cos r=(2n +1)\frac{λ}{2}$

$⇒t=\frac{(2n +1)λ}{4μ\cos r}=\frac{(2n +1)×0.6}{4×1.33×0.8}$

$=0.14 (2n + 1) μm$