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Question

A parallel beam of light of 600 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1.2 m away. It is observed that the first minimum is at a distance of 3mm from centre of the screen. Calculate the width of the slit.

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Solution

The distance of the nth minimum from the centre of the screen is, xn=nDλa
where, D = distance of slit from screen
λ= wavelength of the light
a = width of the slit
For first minimum, n = 1
xn=3×103m
λ=600×109m
D = 1.2 m
3×103=1×1.2×600×109a
a=1×1.2×600×1093×103
=1.2×6×1043
=2.4×104m
=0.24×103m
a=0.24mm


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