Question

Describe biprism experiment to find the wavelength of monochromatic light. Draw the necessary ray diagram for magnified and diminished images of virtual sources.

Answer 1

Fresnel’s biprism experiment can be used to determine the wavelength of a monochromatic light. The fig. shows the experimental arrangement and ray diagram.

Apparatus : An optical bench is used in the biprism expeiment. It consists of a heavy metal platform about 2m in length and carrying four vertical stands to a slits, the biprism, the lens and eyepiece. The stands can be
moved along the bench as well as perpendicular to the bench

Adjustment : The slit S is adjusted to be vertical and narrow. It is illuminated by light from a monochromatic source placed behind it. The light emerging from the slit is made incident on the biprism. The eyepiece stand
is arranged at about 1 m from the slit. The refracting edge of the biprism and the vertical cross-wire of the eyepiece are arranged parallel to the slit and along a straight line. The sit is observed through the eyepiece
and the biprism is slowly rotated aobut the horizontal axis. When its refracting edge becomes exactly parallel to the slit, the interference pattern consisting of alternate bright and dark bands is seen through the
eyepiece. The slit must be suffciently narrow so that the bands are sharp and clear.

Measurement : The wavelength of a monochromatic light is given by `lambda=(barXd)/D, `is the band width or the fringe width d is the distance between the coherent sources and D is the distance between the sources
and the eyepiece. The distance D can be measured directly with the help of the scale marked on the optical bench. To measure the band width X , the micrometer screw fitted to the eyepiece is adjusted such that the vertical cross-wire is made coincide with one of the bright bands. The micromater reading X1 is noted By rotating the screw in the same sense, the vertical cross-wire is made coincide with successive bright bands and the corresponding reading X₂,X₃, X₄.....etc. are noted. The mean value of (X₂–X₁),(X₃–X₂),(X₄–X₃)... etc are noted. The mean value of (X₂–X₁),(X₃–X₂),(X₄–X₃).... etc gives the mean band widthX . To measured the distance between two coherent sources, a convex lens is mounted on the stand between the biprism and the eyepiece. Without disturbing the slit and the biprism, the eyepiece stand is moved along the bench so that the distance the slit and the eyepiece is more than four times the focal length of the lens. The lens stand is moved towards the biprism and its position (L1) is so adjusted that the two magnified images of the slit are seen through the eyepiece by rotating the micrometer screw. The vertical cross-wire in the eyepiece is made to coincide with each image and the corresponding reading is noted. The difference between these two reading gives the distance d1 between the two magnified images. The lens is moved towards the eyepiece and its position (L₂) is so adjusted that two diminished images of the slit are seen through the eyepiece. The distance d₂ between these images is measure as in case of d₁ Then the distance between the two coherent sources is given by `d=sqrt(d_1d_2)`

The wavelength of the monochromatic light is determined by formula i.e  `lambda=(bar(X)d)/D`