Question

A parallel beam of white light is incident normally on a water film of thickness $1.0\times {10}^{-4}\text{cm}$. Find the wavelength in the visible range $(400\text{nm}-700\text{nm})$ which are strongly transmitted by the film.

Refractive index of water, $\mu =1.33$.

• A. $400\text{nm},550\text{nm},700\text{nm}$
• B. $443\text{nm},532\text{nm},665\text{nm}$
• C. $500\text{nm},600\text{nm},700\text{nm}$
• D. $490\text{nm},560\text{nm},630\text{nm}$

Answer 1

The correct option is B $443\text{nm},532\text{nm},665\text{nm}$

For strong transmission,

$2\mu t=n\lambda$

$\Rightarrow \lambda =\frac{2\mu t}{n}$

$\Rightarrow \lambda =\frac{2\times 1.33\times 1\times {10}^{-4}\times {10}^{-2}}{n}=\frac{2.66\times {10}^{-6}}{n}\text{m}=\frac{2660}{n}\text{nm}$

When,

$n=3,{\lambda }_1=887\text{nm}$

$n=4,{\lambda }_2=665\text{nm}$

$n=5,{\lambda }_3=532\text{nm}$

$n=6,{\lambda }_4=443\text{nm}$

$n=7,{\lambda }_5=380\text{nm}$

Hence, option $\left(B\right)$ is the correct answer.