Question

A parallel beam of white light is incident normally on a water film 1.0 × 10⁻⁴ cm thick. Find the wavelengths in the visible range (400 nm − 700 nm) which are strongly transmitted by the film. Refractive index of water = 1.33.

Answer 1

Given,
Wavelength of light used, $\mathrm{\lambda }=400\times {10}^{-9}\mathrm{m}\mathrm{to}700\times {10}^{-9}\mathrm{nm}$
Refractive index of water, $\mathrm{\mu }=1.33$
The thickness of film, $t={10}^{-4}\mathrm{cm}={10}^{-6}\mathrm{m}$
The condition for strong transmission: $2\mathrm{\mu }t=n\lambda$,
where n is an integer.
$\Rightarrow \lambda =\frac{2\mathrm{\mu }t}{n}$
$$\begin{gathered} \Rightarrow \lambda =\frac{2\times 1.33\times {10}^{-6}}{n} \\ =\frac{2660\times {10}^{-9}}{n}\mathrm{m} \end{gathered}$$
Putting n = 4, we get, λ₁ = 665 nm.
Putting n = 5, we get, λ₂ = 532 nm.
Putting n = 6, we get, λ₃ = 443 nm.
Therefore, the wavelength (in visible region) which are strongly transmitted by the film are 665 nm, 532nm and 443 nm.