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A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive indices of the material of the prism for end, green and blue lights are 1.39 , 1.44 and 1.47 respectively. Will the prim separate the colours?

Answer»

Solution :Let the critical ANGLES for red, green and blue lights be `theta_(r), theta_(g), theta_(b)` respectively.
`so, "" sintheta_(r) = (1)/(0.39) or, sintheta_(r) = 0.719 or, theta_(r) = 46^(@)`
`"Again," " " sintheta_(g), = (1)/(1.44) or, sintheta_(g) = 0.694 or, theta_(g) = 44^(@)`
`and sintheta_(b) = (1)/(1.47) or, sintheta_(b) = 0.680 or, theta_(b) = 42.9^(@)` According to Fig. 2.73, the rays are incident normally on the first face and are refracted WITHOUT deviation. So the rays of all the colours are incident on the second face at an angle of incidences `45^(@)` . The green and blue rays are incident on the second face at angles greater than their RESPECTIVE critical angles. So these TWO rays are totally reflected from the second face and after reflection emerge from the base of the prism perpendicular. So the rays of these two colours will not be separated. The ray of red colour is incident on the second face of the prism at an angle less than the critical angle. So it will emerge from the face after refraction through it. Therefore, only the red light becomes separated from the incoming beam of light.


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