question_answer

A ray of light travelling in air is incident at angle \[\theta =30{}^\circ \]on a long rectangular slab of a transparent medium. The point of incidence is origin O of the co-ordinate system shown in figure. The medium has a variable index of refraction \[\mu \left( y \right)\]given by \[\mu ={{\left( 0.25+k{{y}^{-2}} \right)}^{1/2}}\] where\[k=1.0{{m}^{2}}\]. Equation for trajectory of the ray in the medium is\[{{y}^{2}}=ax\]. The value of a is?

Answer:

4.00