- Introduction
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- Refraction through a rectangular glass slab
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- Laws of refraction of light
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- The Refractive Index
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- Refraction by Spherical Lenses
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- Image Formation by Lenses
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- Image Formation in Lenses Using Ray Diagrams
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- Sign Convention for Spherical Lenses
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- Lens Formula and Magnification

- 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.

- 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 v
_{1}be the speed of light in medium 1 and v_{2}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 n_{21}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 n
_{m}of the medium would be

- 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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