Question

For the same value of angle of incidence, the angles of refraction in three media A, B and C are ${15^ \circ }$,${25^ \circ }$ and ${35^ \circ }$ respectively. In which medium would the velocity of light be minimum?

Answer 1

Here we have to use the Snell’s law of refraction and the equation of velocity in a medium to get the answer.
Velocity of light in a medium
$v = \dfrac{c}{n}$
Where,$c$ is the speed of light and $n$ is the refractive index.

Complete step by step answer:
The laws of refraction state that: The refracted ray, the incident ray and the normal of two media at the point of incidence are all on the same plane. A constant is the ratio of the sine of the angle of incidence to the sine of the angle of refraction.In optics, Snell 's law is a relationship between the direction followed by a ray of light as the boundary or surface of separation between two interacting substances is crossed and each of them has a refractive index.
Snell’s law is defined as: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given colour and for the given pair of media.
Mathematically Snell’s law is given by:
$n = \dfrac{{\sin i}}{{\sin r}}$
Also the velocity of light is given by:
$v = \dfrac{c}{n}$
Putting the value of refractive index in this equation we get:
$v = \dfrac{c}{n} \\\ \therefore v= \dfrac{{c \times \sin r}}{{\sin i}} \\\$
From the above relation it is clear that
$v \alpha \sin r$

Hence, the velocity of light is minimum in medium A.

Note: Here we have to see which medium belongs to which angle. Sometimes a larger value may be given first, then we have to match it with the medium.For optical systems, such as fibre optics, Snell’s law is particularly relevant. Snell’s law notes that the proportion of the sines of the incidence and propagation angles is proportional to the refractive index of the interface materials.