A beam of light of `lambda= 600` nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is ...

Options

A. `1.2` cm
B. `1.2`mm
C. `2.4` cm
D. `2.4` mm

Answer

D

Explanation

Condition for first minimum,
`d sin thea_(1)= lambda`
`:. sin theta_(1)=(lambda)/(d)`
but `sin theta_(1)=(x_(1))/(D)`
`:. (x_(1))/(D)=(lambda)/(d)`
`:.x_(1)=(lambdaD)/(d)`
`:.` The distance between first minimum from central maximum on both the sides `=2x_(1)`
`:.2x_(1)=(2lambdaD)/(d)`
`=(2xx600xx10^(-9)xx2)/(1xx10^(-3))`
`=2400xx10^(-6)m=2.4 mm`