Three rays of light red(R) ,green(G) and blue(B) are incident on the surface of a right angled prism  normally on its perpendicular.The refractive indices for the material of tha prism for red,green and blue are 1.39,1.43,1.47 respectively.Trace the path of the rays through the prism.How will the situation change if the rays were falling normally on one of the faces of an equilateral prism?

Hi,

See the diagram

Consider the other two angles of the right angle triangle be 45⁰.

Critical angle for red light is, i_cr = sin^-1 (1/1.39) = 46⁰

Therefore, the red light is refracted. Let, r be the angle of refraction.

1 × sin r = 1.39 × sin 45

=> r = 79.38⁰

Critical angle for green light is, i_cg = sin^-1 (1/1.43) = 44.4⁰

Therefore, the green light is totally internally reflected.

Critical angle for blue light is i_cb = sin^-1 (1/1.47) = 42.9

Therefore, the blue and green both light will undergo in total internal reflection.

Second case: Now all the rays are falling perpendicularly at one surface of equilateral triangle so at the other face they will make incident angle 60°. Using above information about critical angles of red, blue and green light rays 60° is more than the critical angle so three of them undergoes in total internal reflection.