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

The correct option is A $6.738\times {10}^{-5}cm$

If the order of ${\lambda }_1$ is $n$ for ${\lambda }_1>{\lambda }_2$, then the order of ${\lambda }_2$ is $n+1$

Hence, the path difference between interfering waves $=2{\mu }_{oil}t=(n-\frac{1}{2}){\lambda }_1=(n+1-\frac{1}{2}){\lambda }_2$

Here, ${\lambda }_1=7000,{\lambda }_2=5000$

$⟹n=3$

Thus, $t=\frac{(n-\frac{1}{2}){\lambda }_1}{2{\mu }_{oil}}$$=6.738\times {10}^{-5}cm$