White light may be considered to be a mixture of waves with $\lambda$ ranging between $4000 Å, 4667 Å, 5600 Å, 7000 Å, 3900 Å$ and $ 7800 Å$. An oil film of thickness $10,000 Å$ is examined normally by reflected light. If $\mu = 1.4$, then the film appears bright for
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Answer
(a) The film appears bright when the path difference
$(2\mu \,t\,\cos r)$ is equal to odd multiple of $\frac{\lambda }{2}$
i.e. $2\mu t\cos r = (2n - 1)\;\lambda /2$ where $n = 1,\,\,2,\,\,3\,\,.....$
$\therefore \,\,\,\lambda = \frac{{4\mu \,t\,\cos r}}{{(2n - 1)}}$
$ = \frac{{4 \times 1.4 \times 10,000 \times {{10}^{ - 10}} \times \cos 0}}{{(2n - 1)}} = \frac{{56000}}{{(2n - 1)}}{Å}$
$\therefore \,\,\lambda = 56000\,{Å}$ $18666\,{Å},$ $8000\,{Å},$ $6222\,{Å},$ $5091\,{Å},$ $4308\,{Å},$ $3733\,{Å}.$
The wavelength which are not within specified range are to be refracted.
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