Question

White light may be considered to be a mixture of wave with $\lambda$ ranging between $3000 \,?$ and $7800\,?$. An oil film of thickness $10,000\,?$ is examined normally by the reflected light. If $\mu=1.4$, then the film appears bright for

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

Answer 1

Answer: (A)

$4308\,?, 5091 \,?, 6222 \,?$

Answer 2

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