Question

A screen is placed 50cm from a single slit, which is illuminated with 6000Å light. If distance between the first and third minima in the diffraction pattern is 3.0 mm, what is the width of the slit?

Answer 1

Position of nth maxima on a single slit diffraction pattern is given by
`a sin theta = (2n+1) lambda/2`
For small value of `theta, sin theta approx theta = y/D`
`:. (y.a)/D=(2n+1) lambda/2`
`or y=((2n+1))/(2a)D`
:. Distance between third order maxima and first order maxima will be
`Deltay=y_(3)-y_(1)=(2xx(3-1)(lambdaD))/(2a)=(2lambdaD)/a`
Substituting the values, we have
`Deltay=((2)(6xx10^(-7))(0.5))/(3xx10^(-3))=2xx10^(-4)m=0.2mm`