Question

White light may be considered to be a mixture of wavelengths $\lambda$ ranging between $3900\mathring{A}\text{and}7800\mathring{A}.$ An oil film of thickness $10000\mathring{A}$ is examined normally by reflected light. If $\mu =1.4$ , then the film appears bright for-

• A. $4308\mathring{A},5091\mathring{A},6222\mathring{A}$
• B. $4000\mathring{A},5091\mathring{A},5600\mathring{A}$
• C. $4667\mathring{A},6222\mathring{A},7000\mathring{A}$
• D. $4000\mathring{A},4667\mathring{A},5600\mathring{A},7000\mathring{A}$

Answer 1

The correct option is A $4308\mathring{A},5091\mathring{A},6222\mathring{A}$

Given, $\mu =1.4;t=10000\mathring{A}$

In, interference due to reflected light, the film appears bright when the path difference,

$2\mu t\cos r=\text{odd multiple of}\frac{\lambda }{2}$

$\Rightarrow 2\mu t\cos r=(2n-1)\frac{\lambda }{2}$

$\text{where}n=1,2,\mathrm{3...}$

$\therefore \lambda =\frac{4\mu t\cos r}{(2n-1)}$

$=\frac{4\times 1.4\times 10000\times {10}^{-10}\times \cos 0^{\circ }}{(2n-1)}$

$=\frac{56000}{(2n-1)}\mathring{A}$

For, $n=1,2,3,...$

$\therefore \lambda =56000\mathring{A},18666\mathring{A},8000\mathring{A},5091\mathring{A},4308\mathring{A},3733\mathring{A},...$

The wavelength which are not within specified range are to be refracted.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.