Three light rays red (R), green (G) and blue (B) are incident on a right angled prism 'abc' at face 'ab'. The refractive indices of the material of the prism for red, green and blue wavelengths are 1.39 , 1.44 and 1.47 respectively. Out of the time three which colour ray will emerge out of face 'ac' ? Justify your answer. Trace the path of these rays after passing through face 'ab'

Explanation

As `mu=(1)/(sinC),C=sin^(-1)((1)/(mu))`
`"Critical angle for red rays, "=C_(R)=sin^(-1)((1)/(1.39))=46^(@)`
`"Critical angle for green rays"=C_(G)=sin^(-1)((1)/(1.44))=44^(@)`
`"Critical angle for blue rays "=C_(B)=sin^(-1)((1)/(1.47))=42^(@)52.`
As the red, green and blue rays fall at an angle of `45^(@)` on the face AC.
For green and blue rays fall at an angle of `45^(@)` on the face AC.
For green and blue rays, incident angle is greater than the critical angle. Hence, the rays undergo total internal reflection. But in case of red rays, incident angle is smaller than the critical angle the hence, the rays are refracted as shown in figure.