# A beam of light consisting of red, green and blue colours is incident on a right-angled prism…

Q: A beam of light consisting of red, green and blue colours is incident on a right-angled prism. The refractive indices 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 from the green and blue colours

(B) separate the blue colour from the red and green colours

(C) separate all the three colours from one another

(D) not separate even partially any colour from the other two colours.

Ans: (A)

Sol: Let C = critical angle , i = angle of incidence

$\large sinC = \frac{1}{\mu}$

For T.I.R

$\large sini > sinC$

$\large sini > \frac{1}{\mu}$

$\large sin45 > \frac{1}{\mu}$

$\large \frac{1}{\sqrt{2}} > \frac{1}{\mu}$

$\large \mu > \sqrt{2} = 1.414$

Hence , Rays for which $\large \mu > 1.414$ will get T.I.R

So, green & blue will get TIR , only RED comes out of the face