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