# Laws of Refraction of light and Refractive index

## Laws of refraction of light(Snell’s law of refraction)

• Refraction is due to change in the speed of light as it enters from one transparent medium to another.
• Experiments show that refraction of light occurs according to certain laws.
• So Laws of refraction of light are
• The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
• The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given color and for the given pair of media. This law is also known as Snell’s law of refraction.
• If i is the angle of incidence and r is the angle of refraction then $\frac{\sin i} {\sin r} = constant = n$               (1)
This constant value is called the refractive index of the second medium with respect to the first.

## The Refractive Index

• We now know about refraction of light and the extent of the change in direction that takes place in a given pair of media is expressed in terms of the refractive index, the "constant" appearing in equation 1.
• The refractive index is related to an important physical quantity that is relative speed of propagation of light in different media as light propagates with different speeds in different media.
• Consider the figure given below
• Let v1 be the speed of light in medium 1 and v2 be the speed of light in medium 2 then the refractive index of medium 2 with respect to medium 1 is given by the ratio of the speed of light in medium 1 and the speed of light in medium 2. So,

where n21 is the refractive index of medium 2 with respect to medium 1.
• The refractive index of medium 1 with respect to medium 2 is represented as n12. It is given by
• If medium 1 is vacuum or air, then the refractive index of medium 2 is considered with respect to vacuum. This is called the absolute refractive index of the medium.
• If c is the speed of light in the air and v is the speed of light in any medium then refractive index nm of the medium would be

### Prove that the incident angle and the emergent angle in a rectangular glass slab are equal

• In the figure given above ABCD is a rectangular glass slab of thickness AD=BC=t. A ray PQ is incident on it an face AB at point Q, making an angle $PQN_1=i$, called angle of incidence.
• This ray refracts in the glass slab and goes along QR as refracted ray (as shown in the figure) and becomes incident on face DC at point R from inside the slab.
• $\angle RQ{{N}_{2}}=\angle QR{{N}_{3}}=r$ and is called angle of refraction.
• Now the ray emerges or comes out of the slab along RS making $\angle SR{{N}_{4}}=e$ , called the angle of emergence.
• This emergent ray is parallel to the incident ray. This can be proved as follows.
For refraction of Q :- from air to glass \begin{equation*} n=\frac{\sin i}{\sin r} \end{equation*} For refraction at R :- from glass to air $$\frac{1}{n}=\frac{\sin r}{\sin e} \tag{1}$$ or, $$n=\frac{\sin e}{\sin r} \tag{2}$$ from equations 1 and 2 \begin{align} & \sin i=\sin e \\ & \Rightarrow i=e \\ \end{align} angle of incidence = angle of emergence
• It means that incident ray and emergent ray makes equal angles with parallel normal ${{N}_{1}}Q{{N}_{2}}$ and ${{N}_{3}}R{{N}_{4}}$ . Hence incident and emergent rays are parallel.