Question

A parallel beam of white light is incident normally on a water film $1.0\times {10}^{-4}$ cm thick. Find the wavelength in the visible range $(400nm-700nm)$ which are strongly transmitted by the film. Refractive index of water $=1.33$.

• A. $538nm$
• B. $534nm$
• C. $532nm$
• D. $548nm$

Answer 1

The correct option is A $538nm$

For Maximum Transmission

Optical path should be integral multiple of $\lambda$

$\mu 2d=n\lambda$ (Constructive Interference)

where $\mu$ refractive index of film

$\lambda$ wavelength of light

$d$ thickness of film

$\lambda =\frac{2\mu d}{n}$

$\lambda =\frac{2\times 1.33\times 1.0\times {10}^{-4}}{n}cm$

$\lambda =\frac{2.66\times {10}^{-4}}{n}cm$

when

$n=4,{\lambda }_1=665nm$

$n=5,{\lambda }_2=532nm$

$n=6,{\lambda }_3=443nm$