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  • 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 the figure: The refractive indicies of the m

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 the figure:

The refractive indicies 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:
Option: 1 green 
Option: 2 blue and green 
Option: 3 blue
Option: 4 red

Answers (1)

best_answer


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

⇒ Each incident ray will make an angle of 45° with the normal at face PR

⇒ 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^{\circ} the \ light \ ray \ will \ pass\\ \\ \Rightarrow\left(\theta_{ c }\right)_{ Red }=\sin ^{-1}\left(\frac{1}{127}\right) =51.94^{\circ} \\ \ Red \ will \ pass. \\ \\ \Rightarrow\left(\theta_{c}\right)_{\text {Green }}=\sin ^{-1}\left(\frac{1}{1.42}\right) =44.76^{\circ}

\\ \ Green \ will \ not \ pass \\ \\ \Rightarrow\left(\theta_{ C }\right)_{\text {Blue }}=\sin ^{-1}\left(\frac{1}{1.49}\right)=42.15^{\circ} \\ \\ Blue \ will \ not \ pass \\ \\ \Rightarrow So \ only \ red \ will \ pass \ through \ PR.

Posted by

Deependra Verma

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