Question

A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers a glass plate. The wavelength of source can be varied continuously. Complete destructive interference is observed for $\lambda=5000 \,\mathring{A}$ and $\lambda=1000\,\mathring{A}$ and for no other wavelength in between. If $\mu$ of oil is $1.3$ and that of glass is $1.5$, the thickness of the film will be

• A. $6.738 \times 10^{-5} cm$
• B. $5.7 \times 10^{-5} cm$
• C. $4 \times 10^{-5} cm$
• D. $2.8 \times 10^{-5} cm$

Answer 1

Answer: (A)

In this case, both the rays suffer a phase change of $180^{\circ}$ and the conditions for destructive interference is
$2 n d=\left(m+\frac{1}{2}\right) \lambda_{1} $
$2 nd =\left(m+\frac{3}{2}\right) \lambda_{2} $
$\therefore \frac{m+\frac{1}{2}}{m+\frac{3}{2}}=\frac{\lambda_{2}}{\lambda_{1}}=\frac{5000}{7000}=\frac{5}{7} $
and $ d=\frac{\left(m+\frac{1}{2}\right) \lambda_{1}}{2 n}=\frac{2.5 \times 7000}{2 \times 1.3}$
$=6738 \,\mathring{A}=6.738 \times 10^{-5} cm$