The speed of light in substance $X$ is $1.25\times {10^8m/s}$ and that in air is $3\times {10^8m/s}$. The refractive index of this substance will be:(a) 2.4 (b) 0.4 (c) 4.2 (d) 3.75

Speed of light in substance X = $1.25\times {10^8m/s}$ 

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

To find: Refractive index of the substance X.

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 substance X:

$Refractive\ index\ of\ substance\ X=\frac {Speed\ of\ light\ in\ air}{Speed\ of\ light\ in\ substamce\ X}$

Substituting the given value, we get-

$Refractive\ index\ of\ substance\ X=\frac {3.0\times {10^8}m/s}{1.25\times {10^8m/s}}$

$Refractive\ index\ of\ substance\ X=2.4$