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
$2nd=\left(m+\frac{1}{2}\right){\lambda }_1$
$2nd=\left(m+\frac{3}{2}\right){\lambda }_2$
$\therefore \frac{m+\frac{1}{2}}{m+\frac{3}{2}}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{5000}{7000}=\frac{5}{7}$
and $d=\frac{\left(m+\frac{1}{2}\right){\lambda }_1}{2n}=\frac{2.5\times 7000}{2\times 1.3}$
$=6738\mathring{A}=6.738\times 10^{-5}cm$