Question

The absolute refractive indices of glass and water are 4/3 and 3/2 respectively. If the speed of light in glass is 2x108m/s, calculate the speed of light in i) vacuum ii) water

Answer 1

Given that, the refractive index of glass and water with respect to vacuum are 4/3 and 3/2.

Also given that, speed of light in glass is 2 × 10^8 m/s.

Now,

i) For vacuum

Refractive index = (Speed of light in the air or vacuum)/(Speed of light in medium)

4/3 = (Speed of light in vacuum)/(2 × 10^8)

Speed of light in vacuum = 4/3 × 2 × 10^8

Speed of light in vacuum = 2.66 × 10^8 m/s.

ii) For water

Refractive index = (Speed of light in the vacuum)/(Speed of light in water)

3/2 = (2.66 × 10^8)/(Speed of light in water)

Speed of light in water = (2.66 × 10^8)/(3/2)

Speed of light in water = (5.32 × 10^8)/3

Speed of light in water = 1.73 × 10^8 m/s

Answer 2

$\bf{\blue{\bigstar}}$ Answer :

• Given that the absolute refractive indices of glass and water are 4/3 and 3/2 respectively. Speed of light in glass is 2×10⁸ m/s.

We need to find the speed of light in ,

• ( i ) Vacuum

$\bold{Refractive\;Index_{glass}=\frac{Speed\;of\;ligh\;in\;vacuum}{Speed\;of\;light\;in\;glass\;medium} }\\\\\implies \bold{Speed\;of\;light\;in\;vacuum=\frac{4}{3}*2*10^8 }\\\\\implies \bold{\bf{\red{Speed\;of\;light\;in\;vacuum=2.66*10^8\;m/s}}}$

• ( ii ) Water

$\bold{Refractive\;Index_{water}=\frac{Speed\;of\;light\;in\;vacuum}{Speed\;of\;light\;in\;water\;medium} }\\\\\implies \bold{Speed\;of\;light\;in\;water\;=\frac{2.66*10^8}{\frac{3}{2} }\;[From(i)] }\\\\\implies \bold{\bf{\blue{Speed\;of\;light\;in\;water\;=1.73*10^8\;m/s}}}$