Interference fringers are produced by a Fresnel's biprism in the focal plane of reading microscope which is 100 cm from the slit. A lens interposed between the biprism and the microscope gives two images of the slit in two positions.If the images of the slits are 4.05 mm apart in one case, 2.90 mmin the other and the wavelength of light used is 5893 Å, find the distance between two consecutive bands.

Explanation

Here `d_(1)=4.05 mm = 0.405 cm`
`d_(2)=2.09 mm = 0.209 cm`
Distance between the two coherent sources will be
`d=sqrt(d_(1)d_(2))` (Displacement method)
`= sqrt(0.405xx0.209)cm = 0.2909 cm`
Also `D=100 cm`
`lambda = 5893xx10^(-8)cm`
`therefore` Fringe width,
`beta = (D lambda)/(d)`
`= (100xx5893xx10^(-8))/(0.2909)cm`
`= 0.0203 cm`.