Light - Reflection and Refraction | Class 10 CBSE | Web Notes | Part 7: Refractive Index, Refraction by Spherical Lenses

The Refractive Index (n)

It is the ratio of the speeds of light in a pair of media.
It is used to measure the change in direction of a light ray occurring in two media.
Light travels fastest in vacuum (3×10⁸ m/s). In air, there is only a marginal decrease. It reduces considerably in glass or water.
Consider a ray of light travelling from medium 1 into medium 2. The refractive index of medium 2 with respect to medium 1 (n₂₁) is the ratio of speed of light in medium 1 (v₁) to speed of light in medium 2 (v₂).

$Refractive Index Formula n21$

Refractive index of medium 1 with respect to medium 2 is represented as n₁₂.

$Refractive Index Formula n12$

The ratio of the speed of light in vacuum or air (medium 1) to that in medium 2 is called the absolute refractive index. It is represented as n₂.
If c is the speed of light in air and v is the speed of light in the medium, the refractive index of the medium n_m is:

$Absolute Refractive Index Formula$

The absolute refractive index of a medium is simply called its refractive index. For example:
Refractive index of water, n_w = 1.33.

Material Medium	Refractive Index	Material Medium	Refractive Index
Air	1.0003	Crown glass	1.52
Ice	1.31	Canada Balsam	1.53
Water	1.33	Rock salt	1.54
Alcohol	1.36	Carbon disulphide	1.63
Kerosene	1.44	Dense flint glass	1.65
Fused quartz	1.46	Ruby	1.71
Turpentine oil	1.47	Sapphire	1.77
Benzene	1.50	Diamond	2.42

The ability of a medium to refract light is expressed in terms of optical density. It is not the same as mass density. An optically denser medium may not have greater mass density. For example, kerosene is optically denser than water, but its mass density is less than water.

The terms rarer medium and denser medium actually mean optically rarer medium and optically denser medium.
A medium with a larger refractive index is optically denser.
A medium with a lower refractive index is optically rarer.
The speed of light is higher in a rarer medium. So, a ray of light travelling from a rarer medium to a denser medium slows down and bends towards the normal. When it travels from a denser medium to a rarer medium, it speeds up and bends away from the normal.

The glasses used in spectacles and the magnifying glass used by watchmakers are examples of lenses.
A transparent material bound by two surfaces, of which one or both surfaces are spherical, forms a lens.
In a lens with only one spherical surface, the other surface would be plane.
A lens with two spherical surfaces, bulging outwards, is called a double convex lens (simply a convex lens). It is thicker at the middle than at the edges. Such lenses converge light rays, so they are also called converging lenses.
A double concave lens (simply a concave lens) is bounded by two spherical surfaces, curved inwards. It is thicker at the edges than at the middle. Such lenses diverge light rays, so they are also called diverging lenses.

A convex lens or concave lens has two spherical surfaces. Each of them forms a part of a sphere. The centres of these spheres are called centres of curvature of the lens (C₁ & C₂).
An imaginary straight line passing through the two centres of curvature of a lens is called its principal axis.
The central point of a lens is its optical centre (O).
A ray of light through the optical centre of a lens passes without any deviation.
The effective diameter of the circular outline of a spherical lens is called its aperture.
Thin lenses with small apertures: The lenses whose aperture is much less than its radius of curvature and the two centres of curvature are equidistant from the optical centre.

Using a convex lens, focus the light from the Sun on a paper to obtain a sharp, bright, real image of the Sun.
Hold the paper and lens in the same position for a while.
The paper begins to burn and catches fire.
The parallel rays of light from the Sun are converged by the lens at the sharp, bright spot on the paper. This generates heat and causes the burning of the paper.
When several rays of light parallel to the principal axis fall on a convex lens, they undergo refraction from the lens and converge to a point on the principal axis. This point is called the principal focus of the convex lens.
When several rays of light parallel to the principal axis fall on a concave lens, they undergo refraction from the lens and diverge from a point on the principal axis. This point is called the principal focus of the concave lens.
If parallel rays are passed from the opposite surface of the lens, another principal focus is formed on the opposite side. A lens has two principal foci (F₁ & F₂).
The distance of the principal focus from the optical centre of a lens is called its focal length (f). The distance between the position of the convex lens and the position of the image of the Sun gives the approximate focal length of the lens.

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