1. The incident and the refracted ray are at opposite sides of the normal at the point of incidence and all three lie in the same place.
2. For light rays passing from one transparent medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media. That is;

sinisinr= constant. This second law is also known as Snell’s law.

Absolute refractive index

The absolute refractive index or refractive index  of a transparent medium is the ratio of the sine of the incidence angle to the sine of the angle of refraction when light is moving from air to vacuum or into the medium.

The refractive index of a medium is also given by

Example;

A narrow beam of light passes from air into a liquid at an angle of incidence of 55^o. In the liquid, the direction of the beam is turned through 13^o. Calculate;

1. The angle of refraction in the liquid
2. The refractive index of the liquid
3. The speed of light in the liquid, if the speed of light in air is 3.0×10⁸m/s

Solution

1. The liquid should be optically denser than air, so the light bends towards the normal.

Therefore angle of refraction= 55-13=42^o as shown below;

2. Light is moving from air to the medium,

n= sinisinr= sin55sin42= 1.22

note that refractive index is a ratio, so it has no units.

Experimental investigation of Snell’s law; determining refractive index

A large rectangular block is placed on a large sheet of white paper and its outline traced very carefully using a pencil. Two object pins, P₁ and P₂, are stuck on the paper as shown above.

Looking through the side CD, two search pins P₃ and P₄ are stuck on the paper such that P₁, P₂, P₃, and P₄ appear to be in a straight line.

The glass block is removed and the line LMNO and the normal drawn.

Using a protractor, the angles of incidence and refraction (I and r respectively) are measured.

By placing the glass block exactly on the outline and varying the positions of P₁ and P₂, i is varied to obtain corresponding values of r and the results recorded on a well designed table.

It is observed that the ratio sin1sinr is always fairly constant, hence proving Snell’s law. An average values of sinisinr gives the refractive index of the medium.

A more accurate value of the refractive index can be got by plotting a graph of sin I against sin r. this gives a straight line passing through the origin whose gradient corresponds to the refractive index.

The following are some precautions that will ensure accurate results.

•  The pin should be erect and perpendicular to the paper
•  The glass block should be wiped with dry cloth to ensure clear visibility.