State the conditions of total internal reflection. Refractive indices of the given prism material for Red, Blue and Green colours are respectively 1.39, 1.48 and 1.42 respectively. Trace the path of rays through the prism.

Explanation

Critical angle for a light ray is given by `sin i_(c)=(1)/(n) or i_(c) =sin^(-1)((1)/(n))`
`therefore" Critical angle for red ray "(i_(c))_("red")=sin^(-1)((1)/(1.39))`
`-46^(@)`
`"Critical angle for green ray "(i_(c))_("green")=sin^(-1)((1)/(1.44))`
`=44^(@)`
`"and Critical angle for blue ray "(i_(c))_("blue")=sin^(-1)((1)/(1.47))`
`=42^(@)52.`
On the basis of above data, the paths of different coloured rays will be as shown in figure. Blue and green rays are totally internally reflected from the diagonal face of prism but red ray is refracted.