## Tuesday, January 27, 2015

### Refraction of Light Through Prism

The prism is an optical medium which has at least two nonparallel surfaces. Light incidents on one of the surfaces of the prism and emerges out from the other surface. These two surfaces are always nonparallel to each other. The plane surfaces on which light incidents and emerges are called refracting surfaces.

The angle between the two surfaces on which light is incident and emerges is called refracting angle. This is also called angle of prism or apex angle.

The incident light ray, in the absence of the prism can continue in its path without any change in its path. But after passing through the prism it takes a different path. Angle of deviation is the angle between the incident light ray and the emerging light ray.

At any particular point of incidence we can allow the light ray to strikes the surface of the prism. The angle between the normal and the incident light ray is called angle of incidence. As there is a change of media, the light ray will deviate from its path. As the light ray is moving from rarer medium to denser medium, it moves towards the normal inside the prism. The ratio of angle of incidence to angle of refraction at the first surface is equal to refractive index of glass prism with respect to medium.

Inside the prism, the light ray strikes the surface with a particular angle of incidence once again. Again it emerges out from the other surface by moving from denser medium to rarer medium. As a result the light ray moves away from the normal and this light ray is called emerging light ray. The angle between the normal and the emerging light ray is called angle of emergence. Again on the second surface refractive index of the prism with respect to the medium is equal to the ratio of angle of incidence in the second surface to the angle of emergence.

For different angles of incidence, angle of deviation is different. It is practically observed that with the increase of angle of incidence, angle of deviation decreases and reaches to a minimum value. This minimum value of deviation is called angle of minimum deviation. After this minimum deviation, with the increase in angle of incidence angle of deviation further increases as shown in the graph.

When the angle of deviation is minimum, the light ray inside the prism travels parallel to the base of the prism. At this angle , we can derive the equation for the refractive index of a prism with respect to the medium basing on angle of the prism and the angle of minimum deviation is shown below.

For a small angled prism, we can derive the equation for the angle of minimum deviation in terms of angle of prism and refractive index without involving the trignometircal functions like SIN.

Anyway this formula has to be used only when the angle of the prism is small. When the angle of the prism is constant we can write that the angle of minimum deviation is directly proportional to refractive index of the prism as shown below.

As per Cauchy’s formula, we can identify that the refractive index of the present material is inversely proportional to the wavelength of the light approximately. Thus among all the visible colors being the readies having the highest wavelength, its refractive index is lowest.

We shall also understand that among all the visible colors, red deviates least because of its highest wavelength.

Normal incidence and grazing emergence

If a light ray incident the face of a prism with zero angle, that is along the normal drawn, the incidence is called normal incidence. When the light ray emerges, if it emerges along the surface of a prism then it is called the grazing emergence.

For normal incidence, angle of incidence and angle of refraction at the first surface are equal to zero.

The grazing emergence is possible only when the angle of incidence inside the prism is equal to critical angle. As the light ray is emerging at the second surface in a grazing manner, damaging angle is equal to 90°.

By writing the basic conditions of these things in the appropriate equations, we can derive some conditions as shown below.

Grazing incidence and grazing emergence

If the light ray strikes the first surface of the prism along the surface and emerges out of the second surface of the prism again along the surface, it is called grazing incident and grazing emergence. In this case the angle of refraction at the first surface and the angle of incidence at the second surface inside the prism are equal to critical angle.

The angle of incidence as well as the angle of emergence at both the surfaces is equal to 90°. We can derive the equations for critical angle on the minimum deviation is shown in the above diagram.

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