Question

If the difference in velocities of light in glass and water is $0.25\times {10}^{8}m/s,$ find the velocity of light in air.
(Given : ${\mu }_g=1.5,{\mu }_w=4/3$)

Answer 1

Given,

${\mu }_g=1.5$

${\mu }_w=4/3$

Refractive index of medium is defined as the ratio of the velocity of light in medium to the velocity of light in the air,

$\mu =\frac{v}{c}$

Velocity of light in medium,

$v=\mu c$

According to question,

$v_g-v_w=0.25\times {10}^{8}m/s$

${\mu }_{g}c-{\mu }_{w}c=0.25\times {10}^8$

$c(1.5-4/3)=0.25\times {10}^8$

$0.167c=0.25\times {10}^8$

$c=\frac{0.25\times {10}^8}{0.167}$

$c=1.5\times {10}^{8}m/s$