Question

If the difference in velocities of light in glass and water is 0.25 x 10⁸ m/s, find the velocity of light in air.(given : $\mu_{g}$ = 1.5, $\mu_{w}$ = 4/3)
(Ans : 3 x 10⁸ m/s)

Answer 1

In image clear solution is given

Answer 2

Answer:

$3\times 10^8\ m/s$

Explanation:

V = speed of the light in air (assume)

Given that:

$\mu_g$ = refractive index of glass = 1.5

$\mu_w$ = refractive index of water = $\dfrac{4}{3}$

Since the refractive index of water is is less than that in glass. So, the speed of the light is greater in water as compared to that in glass.

Difference in the speed of light in glass and water is given by:

$V_w-V_g=0.25\times 10^{8}\ m/s\\\Rightarrow \dfrac{V}{\mu_w}-\dfrac{V}{\mu_w}=0.25\times 10^{8}\ m/s\\\Rightarrow V(\dfrac{1}{\dfrac{4}{3}}-\dfrac{1}{1.5})=0.25\times 10^{8}\ m/s\\\Rightarrow V(\dfrac{3}{4}-\dfrac{2}{3})=0.25\times 10^{8}\ m/s\\\Rightarrow V(\dfrac{1}{12})=0.25\times 10^{8}\ m/s\\\Rightarrow V=12\times 0.25\times 10^{8}\ m/s\\\Rightarrow V=3\times 10^8\ m/s$

Hence, the speed of the light in the air is $3\times 10^8\ m/s$.