Question

A plane wave of monochromatic light falls normally on a uniform thin film of oil which covers a glass plate. The wavelength of sources can be varied continuously. Complete destructive refraction is observed for $\lambda =5000\dot{A}$ and $\lambda =7000\dot{A}$ 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. $6.378\times {10}^{-5}cm$
• B. $5.7\times {10}^{-5}cm$
• C. $4\times {10}^{-5}cm$
• D. $2.8\times {10}^{-5}cm$

Answer 1

The correct option is A $6.378\times {10}^{-5}cm$

In this case, both the rays suffer a phase change of ${180}^{\circ }$ and the conditions for destructive interference is
2nd = $(m+\frac{1}{2}){\lambda }_1$
2nd = $(m+\frac{3}{2}){\lambda }_2$
$\therefore \frac{m+\frac{1}{2}}{m+\frac{3}{2}}=\frac{{\lambda }_2}{{\lambda }_1}=\frac{5000}{7000}=\frac{5}{7}$ ; m = 2
and $d=\frac{(m+\frac{1}{2}){\lambda }_1}{2n}=\frac{2.5\times 7000}{2\times 1.3}$
$=6738\dot{A}=6.378\times {10}^{-5}cm$