Question

For a parallel beam of monochromatic light of wavelength ${}^{\prime }{\lambda }^{\prime }$, diffraction is produced by a single slit whose width 'a' is of the order of the wavelength of the light. If 'D' is the distance of the screen from the slit, the width of the central maxima will be

• A. $\frac{Da}{\lambda }$
• B. $\frac{2Da}{\lambda }$
• C. $\frac{2D\lambda }{a}$
• D. $\frac{D\lambda }{a}$

Answer 1

Answer: (C)

$\frac{2D\lambda }{a}$

For minima:
$\Delta x=\frac{\lambda }{2}$...(i)
$\frac{asin\theta }{2}=\frac{\lambda }{2}$...(ii)
$sin\theta =tan\theta =\frac{y}{D}$
from equation (ii) and (iii)
$y=\frac{\lambda D}{a}$
the second minima will form $y=\frac{\lambda D}{a}$ exactly below central minima
width of central maxima$=2\frac{\lambda D}{a}$