Question

When white light is incident normally on an oil film of thickness ${10}^{-4}cm$ and refractive index $1.4$ then the wavelength which will not be seen in the reflected system.

• A. $7000\mathring{A}$
• B. $5600\mathring{A}$
• C. $4000\mathring{A}$
• D. All of the above

Answer 1

Answer: (C)

$4000\mathring{A}$

The thickness of film $t={10}^{-4}cm={10}^{-6}m$

The refractive index $\mu =1.4$

For destructive interference in the reflected system

$2\mu t\cos r=(n+1)\lambda$

$\lambda =\frac{2.8\times {10}^{-6}}{n+1}$

For $n=3$

$\lambda =\frac{2.8\times {10}^{-6}}{4}=0.7\times {10}^{-6}=7000\mathring{A}$

For $n=4$

$\lambda =\frac{2.8\times {10}^{-6}}{5}=0.56\times {10}^{-6}=5600\mathring{A}$

For $n=6$

$\lambda =\frac{2.8\times {10}^{-6}}{7}=0.4\times {10}^{-6}=4000\mathring{A}$

$\therefore$ $\lambda =4000\mathring{A}$