Question

A plane wave of monochromatic light falls normally on a uniformly thin film of oil which covers a glass plate. The wavelength of source constructive interference is observed for ${\lambda }_1=5000\stackrel{\circ }{A}$ and ${\lambda }_2=10000\stackrel{\circ }{A}$ and for no other wavelength in between. If $\mu$ of oil is $1.25$ and that of glass is $1.5$, the thickness of film will be ________ $\mu m$.

• A. $0.2$
• B. $0.1$
• C. $0.8$
• D. $0.4$

Answer 1

The correct option is A $0.2$

Given:

${\mu }_o=1.25,{\mu }_g=1.5,{\lambda }_1=5\times {10}^{-7}m={\lambda }_{n+1}$ (No wavelength between destructive interference)

${\lambda }_2=10\times {10}^{-7}m$

The set u is similar to anti-reflective coating.

For destructive interference

$2\mu \cos r=(2n-1)\frac{{\lambda }_n}{2}=\left[2\right(n+1)-1]\frac{{\lambda }_{n+1}}{2}......\left(i\right)$

$(2n-1)\frac{5\times {10}^{-7}}{2}=(2n+1)\frac{10\times {10}^{-7}}{2}$

$n=\frac{3}{2}$....(ii)

For, normal incidence, $cosr=1,$

from (i) and (ii)

$2\mu t=(2\times \frac{3}{2}-1)\frac{{\lambda }_n}{2}={\lambda }_n=5\times {10}^{-7}$

$t=\frac{5\times {10}^{-7}}{2\times 1.25}=2\times {10}^{-7}m$

or the thickness = $0.2\mu m$