The speed of light in water is $2.25\times {10^8}\ m/s$. If the speed of light in vacuum be $3.0\times {10^8}\ m/s$, calculate the refractive index of water.

Given:

Speed of light in water = $2.25\times {10^8}m/s$

Speed of light in vacuum = $3.0\times {10^8}m/s$

To find: Refractive index of water.

Solution:

From the formula for refractive index, we know that-

$Refractive\ index\ of\ a\ medium=\frac {Speed\ of\ light\ in\ vacuum}{Speed\ of\ light\ in\ medium}$

For water:

$Refractive\ index\ of\ glass=\frac {Speed\ of\ light\ in\ vacuum}{Speed\ of\ light\ in\ water}$

Substituting the given value, we get-

$Refractive\ index\ of\ glass=\frac {3.0\times {10^8}m/s}{2.25\times {10^8}m/s}$

$Speed\ of\ light\ in\ glass=1.33$