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Fresnel Mirrors

Fresnel produced the interference fringes by using two plane mirrors M₁ and M₂ arranged at an angle of nearly 180˚ so that their surfaces are nearly (not exactly) coplanar.

A monochromatic source of light S is used. The pencil of light from S incident on the two mirrors, after reflection appears to come from two virtual sources A and B at some distance d apart. Therefore, A and B act as two virtual coherent sources and interference fringes are obtained on the screen. These fringes are of equal width and are alternately dark and bright.

Theory: A and B are two coherent sources at a distance d apart. The screen is at a distance D from the virtual sources. The two reflected beams from the mirrors M₁ and M₂ overlap between E and F (shown as shaded in the diagram) and interference fringes are formed.

Here, D = y₁ + y₂

Fringe width, = λD/d

A point on the screen will be at the centre of a bright fringe, if its distance from C is n λD/d where, n = 0, 1, 2, 3 etc. and it will be at the centre of a dark fringe, if its distance from C is

where, n = 0, 1, 2, 3, …. etc.

For the fringes to be formed, the following conditions must be satisfied. The two mirrors M₁and M₂ should be made from optically flat glass and silvered on the front surfaces. No reflection should take place from the back of the mirrors. The polishing should extend upto the line of intersection of the two mirrors and the line of intersection must be parallel to the line source (slit).

The distance between the two virtual sources A and B can be calculated as follows. Suppose the distance between the points of intersection of the mirrors and the source S is y₁.

θ is known. The angle of separation between A and B is 2θ.

∴ d = 2θ y₁

When white light is used the central fringe C is white, whereas the other fringes on the both sides of C are coloured because the fringe width () depends upon the wavelength. Only the first few coloured fringes are observed and the other fringes overlap. Therefore, the number of fringes seen in the field of wave, with a monochromatic source of light are more, than with white light.