Question

White light may be considered to be a mixture of wave with $\lambda$ ranging between $3000\mathring{A}$ and $7800\mathring{A}$. An oil film of thickness $10,000\mathring{A}$ is examined normally by the 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

Answer: (A)

The film appears bright if the path difference is
$2\mu t\cos r=(2n-1)\frac{\lambda }{2}$
$n=1,2,3,\dots$
$\therefore \lambda =\frac{4\mu t\cos r}{(2n-1)}$
$\lambda =\frac{4\times 1.4\times 10000\times 10^{-10}\cos 0^{\circ }}{(2n-1)}$
$=\frac{56000}{(2n-1)}\mathring{A}$
$\therefore \lambda =56000\mathring{A},18666\mathring{A},11200\mathring{A},8000\mathring{A}$
$6222\mathring{A},5091\mathring{A},4308\mathring{A},3733\mathring{A}$
The wavelengths which are not within specified ranges are to be rejected.