Question

What do you understand by the statement that the refractive index of the glass is 1.5 for white light?

Answer 1

Hint: Refractive index is the ratio of sine of angle of incidence to the sine of angle of refraction. The mathematical expression is $\mu = \dfrac{{\sin i}}{{\sin r}}$ .
Refractive index can also be given as the ratio of speed of light in vacuum to the speed of light in the medium. The mathematical expression is given as $\mu = \dfrac{c}{v}$ where c is the speed of light and the velocity of the light in the medium.

Complete step by step solution:
Here EF is the incident ray and FG is the refracted ray while CD is the normal.

We know that the refractive index can also be given as the ratio of speed of light in vacuum to the speed of light in the medium. This is expressed as $\mu = \dfrac{c}{v}$ where $\mu $ is the refractive index of the medium, c is the speed of light in air and v is the velocity of the light in glass.
Now given that \[\mu = 1.5\] which means that $\mu = \dfrac{c}{v} = 1.5$
$ \Rightarrow \dfrac{c}{v} = 1.5$ which further reduces to $c = 1.5v$ .
Hence from the above expression we can say that the speed of light in vacuum is 1.5 times more than the speed of light in glass.

Note: The expression for refractive index is similar both in terms of wavelength and speed. For wavelength the refractive index is the ratio of wavelength of light in the medium to wavelength of light in vacuum. Refractive index is always greater than 1, 1 being the refractive index of air.