Question

A ray of light from the air suffers partial reflection and refraction at the boundary of water as shown in the figure. In the figure, which of the ray is the correct partially reflected ray?

(a) D
(b) A
(c) C
(d) E

Answer 1

Hint: We have a law that gives the relation of incident ray or incident ray and refracted angle with the refractive index. The refractive index gives the relation between two pair of the medium. The bending of light also depends on the refractive index of the medium. Therefore use of Snell’s law and the law of refraction that shows more the refractive index of the medium, more is the bending of light that takes place towards the normal.

Complete step by step answer:
In this question, a ray is coming from the air and refracted in water and we need to find out which refracted ray is correct out of the given options. The relation between the angle of incidence and the angle of refraction was discovered by Dutch Physicist Willebrord Snell in 1621 and this is known as Snell’s law of refraction.
The given question can be solved by using Snell’s law. This law gives important conclusions about refraction ray which states that
1) At the point of incidence, the incident ray and the refracted ray are on opposite sides of the normal. All these three lie in the same phase.
2) For the given pair of the medium, which is the medium 1 which is air and medium 2 which is water, the ratio of the sine of the angle of incidence to the side of the angle of refraction is constant.

Mathematically, Snell’s law is given as (for a given pair of medium) \[\dfrac{\sin i}{\sin r}=\text{constant}=n.\] n is called a refractive index of the second medium with respect to the first medium. This is known as Snell’s law. So, when light travels from a rarer medium i.e. air to a denser medium i.e. water, the refracted ray bends towards the normal. We know that the refractive index depends on the velocity of light in the medium. Hence, the refractive index is higher in the denser medium and therefore the angle of refraction in the denser medium should be lesser than the angle of incidence.
As you can see in the figure given below,

Ray A has the smallest angle, tracing from the normal. Hence, ray A is the correct refracted ray.
Hence, option (b) is the right answer.

Note:
The bending of refracted rays depends on the density of the medium. If the refracted ray bends away from the normal, then the incident ray must pass from a denser medium to a rarer medium. If the angle of incidence is zero, i.e. i = 0, i.e. the incident ray incident normally at the boundary between the two media, then the refracted ray does not change its direction and hence does not get refracted.