Question

What is the speed of light in the medium whose refractive index is 3/2? Given speed of light is 3×10^8 m/s​

Answer 1

Given :-

◉ Speed of light, c = 3 × 10^8 m/s

◉ Refractive index of medium = 3/2

To Find :-

◉ Speed of light in the given medium

Solution :-

We know,

Refractive Index in terms of Speed of Light

⇒ Speed of Light in Air / Speed of Light in medium

Given, Refractive Index = 3/2

Now,

⇒ 3/2 = 3 × 10^8 / v

⇒ v = 2 × 10^8 m/s

Hence, Speed of Light in the given medium is 2 × 10^8 m/s

More Information :-

◉ Refractive Index of a medium m is the ratio of speed of light in air and the speed of light in the medium m.

◉ Refractive Index is also equal to ratio of sine of the angle of incidence and sine of the angle of refraction. which is also known as Snell's Law.

Answer 2

Given ,

Refractive index of medium = 3/2

Speed of light = 3 × (10)^8 m/s

We know that ,

$\boxed{ \sf{Refractive \: index \: of \: medium \: (n) = \frac{speed \: of \: light \: in \: vaccum }{speed \: of \: light \: in \: medium } }}$

Thus ,

$\sf \mapsto \frac{3}{2} = \frac{3 \times {(10)}^{8} }{speed \: of \: light \: in \: medium} \\ \\ \sf \mapsto speed \: of \: light \: in \: medium = 2 \times {(10)}^{ 8} \: m{s}^{ - 1}$

$\sf \therefore \underline{The \: speed \: of \: light \: in \: medium \: is \: 2 \times {(10)}^{ 8} \: m{s}^{ - 1} }$