The refractive index of diamond with respect to air is $2.42$. What will be the refractive index of air with respect to diamond ?

The correct option is C $0.41$
Step 1, Given data

Refractive index of diamond, ${\mu }_{d,a}=2.42$

Step 2, Finding the refractive index of air w.r.t diamond

Let the refractive index of air with respect to diamond be ${\mu }_{a,d}$.

From definition of refractive index,
we can write, ${\mu }_{d,a}=\frac{{\mu }_d}{{\mu }_a}$
In the same way ${\mu }_{a,d}=\frac{{\mu }_a}{{\mu }_d}$

From above both equation we can write

$⟹{\mu }_{a,d}=\frac{1}{{\mu }_{d,a}}$

Putting all the values
${\mu }_{a,d}=\frac{1}{2.42}$
${\mu }_{a,d}=0.4132$

Hence the refractive index of air with respect to the diamond is 0.4132.