10. LIGHT – REFLECTION AND REFRACTION

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 ms^–1). In air, there is only marginal decrease. It reduces considerably in glass or water.

Consider a ray of light travelling from medium 1 into medium 2. Then the refractive index of medium 2 with respect to medium 1 (n₂₁) is the ratio of speed of light in medium 1 (v₁) and speed of light in medium 2 (v₂).

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

The ratio of the speed of light in vacuum or air (medium 1) and in the medium 2 is called 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

The absolute refractive index of a medium is simply called its refractive index. E.g.

Refractive index of water, n_w = 1.33.

Refractive index of crown glass, n_g =1.52.

Absolute refractive index of some material media

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. E.g., kerosene is optically denser than water, but its mass density is less than water.

The terms rarer medium & denser medium actually mean optically rarer medium and optically denser medium.

Medium of larger refractive index is optically denser.

Medium of 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.

Refraction by Spherical Lenses

The glasses used in spectacles and 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, it is also called converging lens.

A double concave lens (simply a concave lens) is bounded by two spherical surfaces, curved inwards. It is thicker at 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 curvatures are equidistant from the optical centre.

Incidence of parallel rays on a lens:

Using a convex lens, focus the light from the Sun on a paper. 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. It generates heat and causes burning of 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 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 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 position of convex lens and position of image of the Sun gives approximate focal length of the lens.