The refractive index of glass for light going from air to glass is $\frac {3}{2}$. The refractive index for light going from glass to air will be:(a) $\frac {1}{3}$ (b) $\frac {4}{5}$ (c) $\frac {4}{6}$ (d) $\frac {5}{2}$

(c) $\frac {4}{6}$    

Explanation:

Given: 

Refractive index of glass for light going from air to glass, $_{air}\ {n}_{glass}$ = $\frac {3}{2}$

To find: Refractive index for light going from glass to air, $_{glass}\ {n}_{air}$.

Solution:

Refractive index of material 2 with respect to material 1 is given by:

$_{1}\ {n}_{2}=\frac {Speed\ of\ light\ in\ medium\ 1}{Speed\ of\ light\ in\ medium\ 2}$

By the same argument, the refractive index of medium 1 with respect to medium 2 is given by: 

$_{2}\ {n}_{1}=\frac {Speed\ of\ light\ in\ medium\ 2}{Speed\ of\ light\ in\ medium\ 1}$

In relation to $_{1}\ {n}_{2}$, the above equation can also be written as:

From the above equation, we can conclude that the refractive index of a medium 1 with respect to medium 2 is reciprocal to the refractive index of medium 2 with respect to medium 1.

Now, substituting the value of $_{2}\ {n}_{1}$ we get-

$_{2}\ {n}_{1}=\frac {1}{\frac {3}{2}}$

$_{2}\ {n}_{1}=\frac {2}{3}$

Note: To get the answer among the given options, we need to multiply $\frac {2}{3}$ by $\frac {2}{2}$, then we get $\frac {4}{6}$.