JEE PYQ: Ray Optics Question 7
Question 7 - 2021 (18 Mar Shift 2)
Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in figure.
The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49 respectively. The colour of the ray(s) emerging out of the face PR is:
(1) green
(2) red
(3) blue and green
(4) blue
Show Answer
Answer: (2)
Solution
Assuming that the right angled prism is an isoceles prism, so the other angles will be 45°. $\Rightarrow$ Each incident ray will make an angle of 45° with the normal at face PR. $\Rightarrow$ The wavelength corresponding to which the incidence angle is less than the critical angle, will pass through PR. $\Rightarrow \theta_C =$ critical angle $\Rightarrow \theta_C = \sin^{-1}\left(\frac{1}{\mu}\right)$ $\Rightarrow$ If $\theta_C \geq 45°$, the light ray will pass. $\Rightarrow (\theta_C){\text{Red}} = \sin^{-1}\left(\frac{1}{1.27}\right) = 51.94°$ Red will pass. $\Rightarrow (\theta_C){\text{Green}} = \sin^{-1}\left(\frac{1}{1.42}\right) = 44.76°$ Green will not pass. $\Rightarrow (\theta_C)_{\text{Blue}} = \sin^{-1}\left(\frac{1}{1.49}\right) = 42.15°$ Blue will not pass. $\Rightarrow$ So only red will pass through PR.
BETA
