System For Observing Interference Phenomenon: Fresnel Biprism

To determine the separation between the two virtual sources ( d ), a convex lens of short focal length is introduced between the biprism and the eye piece, keeping the distance between the slit and eyepiece to be more than four times the focal length of lens. The lens is moved along the length of bench to a position where two images of slits are seen in the plane of cross wires of eye piece. The distance between these two images of slit is measured by setting the vertical cross wire successively on each of images and recording the two positions of cross wire using micrometer. Let this separation be d₁ . Now the lens is moved such that for another position of lens, again two images of slit are seen on eye piece. Let d₂ be the separation between these two images. Since these two positions of lens are conjugate, the separation between the virtual source ‘d ' is given as

Fig.C:Determination of 'd' in Fresnel Biprism experiment

o determine the wavelength of the source, we need to know the fringe width. For this, the convex lens is removed and the experimental arrangement is as shown in fig. Now we move the eyepiece, so that fringes with good contrast are visible on eyepiece. The fringe width is measured by setting the cross wire of eyepiece on every fifth bright fringe and recording the position using micrometer screw. The average fringe width () is then determined by averaging the distance between every 5 fringes and then by dividing by 5. Knowing , d, D, can be determined.

To determine the thickness of transparent thin sheet (mica), the monochromatic source is replaced by white light source. In this case the fringe pattern consists of several fringe patterns corresponding to all wavelength and the resultant of this is a central white fringe surrounded by dark region.

The position of this central white fringe is recorded by focusing the cross wire of eye piece on it and taking this reading of micrometer scale. Now mica sheet is introduced in the path of one wave. (such that it blocks the one half of biprism). By doing it the one wave traverse an extra optical path and the path difference between the two waves is not same and entire fringe pattern shifts. The central white fringe is now shifted to another position of cross wire. If ‘S' is the shift in position of white fringe and be the refractive index of mica sheet, thickness ‘t' of mica sheet is given by

                        cm