A source of monochromatic light of wavelength 0.6 `mu`m is placed at a distance 0.3 m from a narrow slit, the distance between consecutive maxima is found to be 0.15 m m on a screen 0.5 m from the slit. Calculate width of the slit.

Answer

2

Explanation

This is a case of Fresnel diffraction at a narrow slit. The distance of the `n^(th)` bright fringe from the centre of the anti-shadow is given by `x_(n)=((2n-1)D lambda)/(2d)`
`:.x_(n-1) =((2n-3) Delta lambda)/(2d)`
`:.x_(n) -x_(n-1) =(Delta lambda)/(d)`
This is independent of n.
Here fringes are of constant width. Let this constant be `beta`.
Then `beta` (fringe width) `=(Delta lambda)/(d)`
`:.d=(Delta lambda)/(beta) =(0.5 xx 0.6 xx 10^(-6))/(0.15) = 2xx 10^(-6)m = 2 mum`