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A parallel beam of green light of wavele...

A parallel beam of green light of wavelength 546 nm passes through a slit of width 0.40mm. The transmitted light is collected on a screen 40 cm away. Find the distance between the two first order minima.

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The minima occur at an angular deviation theta given by `b sintheta=nlamda, where n` is an integer. For the first order minima,n=+-1` so that `sintheta=+-lamda/b`. As the fringes are observed at a distance much larger than the width of the slit, the linear distances from the central maximum are given by
`x=Dtantheta`
`=Dsintheta=+-(lamdaD)/b`
Thus the minima are formed at distance `(lamdaD)/b` from the central maximum on its two sides. The separation between the minima is
`(2lamdaD)/2=(2xx546xx10^-9mxx40xx10^-2m)/(0.40xx0^-3m)=1.1mm.
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