Light enters from air into diamond which has a refractive index of $2.42$. Calculate the speed of light in diamond. The speed of light in air is $3.0\times {10^8}\ ms^{-1}$.

Refractive index of diamond = $2.42$

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

To find: Speed of light in diamond.

Solution:

From the formula for refractive index, we know that-

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

For diamond:

$Refractive\ index\ of\ diamond=\frac {Speed\ of\ light\ in\ air}{Speed\ of\ light\ in\ diamond}$

Substituting the given value, we get-

$2.42=\frac {3.0\times {10^8}m/s}{Speed\ of\ light\ in\ diamond}$

$Speed\ of\ light\ in\ diamond=\frac {3.0\times {10^8}m/s}{2.42}$

$Speed\ of\ light\ in\ diamond=1.239\times {10^8}m/s$