Question

(i) Define the term refractive index of a medium in terms of velocity of light.
(ii) A ray of light moves from a rarer medium to denser medium as shown in diagram. Write down the number of the ray which represents the partially reflected ray.

Answer 1

Hint: Study the ray diagram given in the question properly. Find the definition of refractive index of a medium in terms of velocity of light starting from the Snell’s law of refraction. Find the partially reflected ray from the diagram using the concept of refraction.

Complete step-by-step answer:
(i) Snell’s law describes that the ratio of sine of incident angle to the sign of refracted angle is a constant for the given media.
$\dfrac{\sin i}{\sin r}={{n}_{21}}$
Where, i is the angle of incidence and r is the angle of refraction.
${{n}_{21}}$ is a constant and is called the refractive index of the second medium with respect to the first medium.
Refractive index can be defined as the ratio of velocity of light in the two media through the interface of which light is passed.
${{n}_{12}}=\dfrac{1}{{{n}_{21}}}$
Where, ${{n}_{12}}$ is the refractive index of the first medium with respect to the second medium.
Relative refractive index can be defined as the ratio of velocity of light in the given media with respect to the velocity of light in vacuum. We can write
$n=\dfrac{c}{v}$
Where n is the relative refractive index of the medium, c is the speed of light in vacuum and v is the speed of light in the given medium.
(Ii) When a beam of light encounters the interface of two mediums, a part of the light is reflected back to the first medium and the other passes through the second medium. The part of light which is reflected back to the first medium is called the partially reflected ray.
In the diagram given in the question the partially reflected ray is represented by the ray 2.

Note: we can define the refractive index as the ratio of velocities in the two media. So refractive index is a unitless quantity (ratio or just a number).
Hence, we can say that the refractive index is dimensionless.
Dimension of refractive index is $\left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right]$