Question

When the angle of incidence on the material is $60^{\circ}$, the reflected light is completely polarised. The velocity of the refracted ray inside the material is.

Answer 1

Hint: Brewster was capable of determining that the medium's refractive index is numerically equal to the tangent angle of polarization. Brewster's law gives the relationship of light waves at the highest polarization angle of light.

Complete answer:
Given: incidence angle is $60^{\circ}$.
$\theta_{i} = 60^{\circ}$
The reflected light is completely polarised, then the incidence angle is equal to the polarising angle.
$\theta_{i} = \theta_{p}$
$\implies \theta_{p} = 60^{\circ} $
Brewster law gives,
$\mu = \tan \theta_{p}$
$\mu$ is the refractive index.
$\theta_{p}$ is a polarising angle.
Put $\theta_{p}$ in the above formula.
$\mu = \tan 60^{\circ} $
$\mu = \sqrt{3}$
Refractive index is defined as the ratio of speed of light in air to that of speed of light in medium.
$\dfrac{c}{v} = \sqrt{3}$
$\implies v = \dfrac{c}{\sqrt{3}}$
Put $c = 3 \times 10^{8} ms^{-1}$ in the above formula.
$\implies v = \dfrac{3 \times 10^{8}}{\sqrt{3}}$
$v = \sqrt{3} \times 10^{8} m s^{-1}$
The velocity of the refracted ray inside the material is $ 1.732 \times 10^{8} m s^{-1}$.

Note: Brewster’s law gives a relationship for light waves stating that the maximum polarization of a ray of light may be obtained by letting the beam fall on an outside of a transparent medium in such a system that the refracted ray creates an angle of $90^{\circ}$ with the reflected beam.