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,

\[\lambda = 400 \times {10}^{- 9} m\text{ to }700 \times {10}^{- 9} nm\]

Refractive index of water,

\[\mu = 1 . 33\]

The thickness of film,

\[t = {10}^{- 4} cm = {10}^{- 6} m\]

The condition for strong transmission

\[2\mu t = n\lambda\]

where n is an integer.

\[\Rightarrow   \lambda = \frac{2\mu t}{n}\]

\[\Rightarrow \lambda = \frac{2 \times 1 . 33 \times {10}^{- 6}}{n}\]

\[ = \frac{2660 \times {10}^{- 9}}{n} m\]

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.