Question

The refractive index of water and glass are 1.2 and 1.5 with respect to air, respectively. Calculate the refractive index of glass with respect to water. (Take speed of light in air, c = 3 × 108 m/s)

• A. 1.5
• B. 1.25
• C. 1.75
• D. 2

Answer 1

The correct option is B 1.25

We know that,
Refractive index of medium 2 with respect to medium 1, ${}_1{\mu }_2=\frac{\text{sped of light in medium 1}}{\text{speed of light in medium 2}}$

We have to find the refractive index of glass with respect to water, so according to the above equation first we need to find the speed of light in water and glass.

Given, Speed of light in air $=3\times {10}^{8}m/s$
So, Refractive index of water with respect to air,

${}_{air}{\mu }_{water}=\frac{\text{sped of light in air}}{\text{speed of light in water}}$
$1.2=\frac{3\times {10}^8}{\text{speed of light in water}}\text{Therefore, speed of light in water}=2.5\times {10}^{8}m/s$
$\text{Similarly, Refractive index of glass with respect to air,}{}^{}{}_{air}{\mu }_{glass}=\frac{\text{sped of light in air}}{\text{speed of light in glass}}$
$1.5=\frac{3\times {10}^8}{\text{speed of light in glass}}\text{Therefore, speed of light in glass}=2\times {10}^{8}m/s\text{Hence, Refractive index of glass with respect to water is}{}^{}{}_{water}{\mu }_{glass}=\frac{\text{sped of light in water}}{\text{speed of light in glass}}=\frac{2.5\times {10}^8}{2\times {10}^8}=1.25$