Question

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

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

Answer 1

Answer: (D)

Here, $\lambda=600 \,nm =600 \times 10^{-9} \,m$
$a=1 mm =10^{-3} m , D=2 m$
Distance between the first dark fringes on either side of the central bright fringe is also the width of central maximum.
Width of central maximum $=\frac{2 \lambda D}{a}$
$=\frac{2 \times 600 \times 10^{-9} m \times 2 m }{10^{-3} m } $
$=24 \times 10^{-4} m $
$=2.4 \times 10^{-3} m $
$=2.4\, mm$