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?

Options

A. `0.1mm`
B. `0.2mm`
C. `0.4mm`
D. `0.8mm`

Answer

B

Explanation

Position of first minima on a single slit diffraction pattern is given by
`d sin theta = n lambda`
For small value of `theta, sin theta ~~ theta = (y)/(D)`
`:. (y.a)/(D) = n lambda or y= (n lambda D)/(a)`
`:.` Distance between third order minima and first order minima will bew
`Delta y = y_(3)-y_(1) = ((3-1)(lambda D))/(a) = (2lambda D)/(a)`