Question

The velocity of light in diamond is $1.25\times {10}^8$ m/s; Find the refractive index of diamond with respect to water (Refractive index of water w.r.t. air is $1.33$).

Answer 1

${\mu }_{wA}=\frac{\text{Velocity of light in air}\left(v_A\right)}{\text{Velocity of light in water}\left(v_W\right)}{v}_w=\frac{v_A}{{\mu }_{wA}}=\frac{3\times {10}^8}{1.33}=2.25\times {10}^8$

${\mu }_{DW}=\frac{\text{Velocity of light in water}\left(v_w\right)}{\text{Velocity of light in diamond}\left(v_D\right)}{\mu }_{DW}=\frac{2.25\times {10}^8}{1.25\times {10}^8}=1.80$

Where${\mu }_{DW}\text{and}{\mu }_{WA}=$refractive index of diamond with respect to water and refractive index of water with

respect to air respectively