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Thermodynamics

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Fresnel Biprism

Fresnel used a biprism to show interference phenomenon. The biprism abc consists of two acute angled prisms placed base to base. Actually, it is constructed as a single prism of obtuse angle of about 179˚. The acute angle on both sides is about 30’. The prism is placed with its refracting edge parallel to the line source S (slit) such that Sa is normal to the face bc of the prism. When light falls from S on the lower portion of the biprism it is bent upwards and appears to come from the virtual source B. Similarly light falling from S on the upper portion of the prism is bent downwards and appears to come from the virtual source A. Therefore A and B act as two coherent sources. Suppose the distance between A and B = d.

If a screen is placed at C, interference fringes of equal width are produced between E and F but beyond E and F fringes of large width are produced which are due to diffraction. MN is a stop to limit the rays. To observe the fringes, the screen can be replaced by an eye-piece or a low power microscope and fringes are seen in the field of view. If the point C is at the principal focus of the eyepiece, the fringes are observed in the field of view.

Theory: For complete theory, the point C is equidistant from A and B. Therefore, it has maximum intensity. On both sides of C, alternately bright and dark fringes are produced. The width of the bright fringe or dark fringe, = λD/d. Moreover, any point on the screen will be at the centre of a bright fringe if its distance from C is nλD/d, where, n = 0, 1, 2, 3, …. etc. The point will be at the centre of a dark fringe if its distance from C is

(2n+1)λD/2d,

where, n = 0, 1, 2, 3, …. etc.

Determination of wavelength of light: Fresnel’s biprism can be used to determine the wavelength of a given source of monochromatic light.

A fine vertical slit S is adjusted just close to a source of light and the refracting edge is also set parallel to the slit S such that bc is horizontal. They are adjusted on an optical bench.

A micrometer eyepiece is placed on the optical bench at some distance from the prism, to view the fringes in its focal plane (at its cross wires).

Suppose the distance between the source and the eyepiece = D and the distance between the two virtual sources A and B = d. The eyepiece is moved horizontally (perpendicular to the length of the bench) to determine the fringe width. Suppose, for crossing 20 bright fringes from the field of view, the eyepiece has moved through a distance l.

Then the fringe width, = l/20

But the fringe width, = λD/D

∴ λ = βd/D