JEE Main & Advanced Physics Ray Optics Question Bank Topic Test - Refraction of Light Through Plane Surfaces

A glass slab has the left half of refractive index \[{{n}_{1}},\] and the right half of \[{{n}_{2}}=3{{n}_{1}}\]. The effective refractive index of the whole slab is

A) \[\frac{{{n}_{1}}}{2}\]

B) \[2n\]

C) \[\frac{3{{n}_{1}}}{2}\]

D) \[\frac{2{{n}_{1}}}{3}\]

Correct Answer: C

Solution :

[c] Total time taken to travel distance d is:

\[\frac{d}{2{{n}_{1}}}+\frac{d}{2{{n}_{2}}}=d\left( \frac{{{n}_{1}}+{{n}_{2}}}{2{{n}_{1}}{{n}_{2}}} \right)=\frac{d}{{{n}_{eff}}};\]

\[{{n}_{2}}=3{{n}_{1}}\Rightarrow \,{{n}_{eff}}=\frac{3}{2}{{n}_{1}}\]

\[=\frac{6\times {{10}^{5}}cm}{1.0003-1}\]\[=0.2cm=2mm\]