Question

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 the red colour part from the green and blue colours
• B. Separate the blue colour part from the red and green colours
• C. Separate all the three colours from one another
• D. Not separate the three colours at all

Answer 1

The correct option is A Separate the red colour part from the green and blue colours

Since the beam of light rays is incident normally at the surface $AB$, it will reach undeviated at the surface $AC$.


From geometry, the angle of incidence at $AC$ is, $i={45}^{\circ }$
For red colour,
$i_c={\sin }^{-1}\left(\frac{{\mu }_r}{{\mu }_d}\right)$
$\Rightarrow i_c={\sin }^{-1}\left(\frac{1}{1.39}\right)$
$\Rightarrow i_c={\sin }^{-1}\left(0.72\right)\approx {46.1}^{\circ }$ ..........$\left(1\right)$
For green colour,
$\Rightarrow i_c={\sin }^{-1}\left(\frac{1}{1.44}\right)$
$\Rightarrow i_c={\sin }^{-1}\left(0.69\right)\approx {43.6}^{\circ }$ ..........$\left(2\right)$
For blue colour,
$\Rightarrow i_c={\sin }^{-1}\left(\frac{1}{1.47}\right)$
$\Rightarrow i_c={\sin }^{-1}\left(0.68\right)\approx {42.8}^{\circ }$ ..........$\left(3\right)$
From $\left(1\right)$, $\left(2\right)$ and $\left(3\right)$, we can see that, for red colour, $i<i_c$, and for green and blue colour, $i>i_c$.
Thus, green and blue colour will suffer total internal reflection while red will emerge out and hence get separated from green and blue colours.

Tip: You don't need to learn or find the exact $\sin$ values. Just remember $\sin 45=0.707$ and you can compare the others relatively.