1.

The angular width of the central maximum in a single slit diffraction pattern is 60^(@). The width of the slit is 1 mu m The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it. Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance ? (i.e. distance between the centres of each slit)

Answer»

`25 MU m`
`50 mu m`
`75 mu m`
`100 mu m`

Solution :`2 theta=60^(@)`
`:. theta=30^(@)`
For fringe of first order minimum
`d sin theta= lambda`
`:. d sin 30^(@) lambda,`
`:. Dxx(1)/(2)= lambda`
`:. lambda=(d)/(2)`
WIDTH of fringe `beta=(lambdaD)/(d.)`
`d.=(lambdaD)/(beta)`
`=(d)/(2)XX(D)/(beta)`
`=(10^(-6))/(2)xx(50xx10^(-2))/(1xx10^(-2))`
`=25xx10^(-6)m`
`:.d.=25 mum`


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