Laws of Refraction of light and Refractive index

Laws of refraction of light(Snellís 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 Snellís 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
    refraction of light ray fron rarer medium to denser medium
  • 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,
    refractive index of medium 2 with respect to medium 1
    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
    refractive index of medium 1 with respect to medium 2
  • 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 refractive index of medium

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

Laws of Refraction of light
Figure :- Refraction of light through rectangular glass slab

  • 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 \begin{equation} \frac{1}{n}=\frac{\sin r}{\sin e} \tag{1} \end{equation} or, \begin{equation} n=\frac{\sin e}{\sin r} \tag{2} \end{equation} 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.

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Class 10 Maths Class 10 Science

Practice Question

Question 1 Which among the following is not a base?
B) $NH_4OH$
C) $C_2H_5OH$
Question 2 What is the minimum resistance which can be made using five resistors each of 1/2 Ohm?
A) 1/10 Ohm
B) 1/25 ohm
C) 10 ohm
D) 2 ohm
Question 3 Which of the following statement is incorrect? ?
A) For every hormone there is a gene
B) For production of every enzyme there is a gene
C) For every molecule of fat there is a gene
D) For every protein there is a gene

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