A beam of light consisting of red, green and blue colours is incident on a right-angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are $1.39$, $1.44$and $1.47$ respectively.



The prism will:

• A

  Separate all the three colours from one another
• B

  Not separate the three colours at all
• Correct answer
  C

  Separate the red colour part from the green and blue colours
• D

  Separate the blue colour part from the red and green colours

Solution

For Total internal reflection, \(i > i_{\mathrm{c}}\) so, \(\sin i > \sin i_c\) \(\sin 45^{\circ} > \frac{1}{\mu}\) $\Rightarrow \mu =\sqrt{2}$ $\Rightarrow \mu =1.414$ Since $\mu$ of green and violet is greater than $1.414$, so they will undergo total internal reflection. But red colour will be refracted. So the prism will separate red colour from the green and blue colours.

Hence, the correct answer is option: 'C'.