Three rays of light, namely red R , green ( G ) and blue ( B ) are incident on the face P Q of a right angled prism P Q R as shown in figure. The refractive indices of the material of the prism for re

Question

Three rays of light, namely red R , green ( G ) and blue ( B ) are incident on the face P Q of a right angled prism P Q R 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 P R is :

TestHub · Accepted Answer

Assuming that the right angled prism is an isoceles prism, so the other angles will be $45 °$ each.

$\Rightarrow$ Each incident ray will make an angle of $45 °$ with the normal at face $P R$ .

$\Rightarrow$ The wavelength corresponding to which the incidence angle is less than the critical angle, will pass through $P R$ .

$\Rightarrow θ_{C} =$ critical angle

$\Rightarrow θ_{C} = \sin^{- 1} (\frac{1}{μ})$

$\Rightarrow$ If $θ_{C} \geq 45 °$

the light ray will pass

$\Rightarrow {(θ_{C})}_{Red} = \sin^{- 1} (\frac{1}{1.27}) = 51.94 °$

Red will pass.

$\Rightarrow {(θ_{C})}_{Green} = \sin^{- 1} (\frac{1}{1.42}) = 44.76 °$

Green will not pass

$\Rightarrow {(θ_{C})}_{Blue} = \sin^{- 1} (\frac{1}{1.49}) = 42.15 °$

Blue will not pass

$\Rightarrow$ So only red will pass through $P R$ .

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