question_answer

A rectangular glass slab AB CD of refractive index  \[{{n}_{1}}\] is immersed in water of refractive index \[{{n}_{2}}({{n}_{1}}>{{n}_{2}}).\] A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence \[{{\alpha }_{\max }}\] such that the ray comes out only from the other surface CD is given by

A) \[{{\sin }^{-1\grave{\ }}}\left[ \frac{{{n}_{1}}}{{{n}_{2}}}\cos \left( {{\sin }^{-1}}\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right) \right) \right]\]

B) \[{{\sin }^{-1\grave{\ }}}\left[ {{n}_{1}}\cos \left( {{\sin }^{-1}}\left( \frac{1}{{{n}_{2}}} \right) \right) \right]\]

C) \[{{\sin }^{-1}}\left( \frac{{{n}_{1}}}{n{{  }_{2}}} \right)\]

D) \[{{\sin }^{-1}}\left( \frac{{{n}_{2}}}{n{{  }_{1}}} \right)\]