Question

Find out the velocity of light in water if the refractive index of water is 4/3.(velocity

of light in air is 3×108

ms-1)​

Answer 1

Find the answer in the figure attached.

Answer 2

Required Answer:-

Given:

• The refractive index of water = 4/3
• Speed of light in air = 3 × 10⁸ m/s

To Find:

• The speed of light in water.

Solution:

We know that, refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium.

So,

$\dag\ \boxed{\tt \mu= \dfrac{Speed\:of\:light\:in\:air\:(c)}{Speed\:of\:light\:in\:medium\:(V)}}$

Here,

$\tt\implies \mu=\dfrac{4}{3}$

$\tt c=3\times {10}^{8}\:ms^{-1}$

→ Let the velocity of light in water be V m/s.

Plugging the values in the formula, we get,

$\tt\implies\dfrac{4}{3}=\dfrac{3\times 10^{8}}{V}$

$\tt\implies4V=3\times3\times 10^{8}$

$\tt\implies4V=9\times 10^{8}$

$\tt\implies V=\dfrac{9}{4}\times 10^{8}$

$\tt\implies V=2.25\times 10^{8}\:ms^{-1}$

→ Therefore, the speed of light in water is 2.25 × 10⁸ m/s

Answer:

• The speed of light in water is 2.25 × 10⁸ m/s.