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. 2D a/λ
• B. 2Dλ/a
• C. Dλ/a
• D. Da/λ

Answer 1

The correct option is B

2Dλ/a

For a parallel beam of monochromatic light of wavelength $\lambda$, diffraction is produced by a single slit whose width 'a' is of the order of the wavelength we have

$sin\theta =\frac{\lambda }{a}$.....(1)

where $\theta$ is the angle subtended by the first minima and the central maxima at the slit.

$\therefore 2sin\theta =\frac{2\lambda }{a}$......(2)

If x is the width of the central maxima, we have

$\frac{x}{D}=\frac{2\lambda }{a}$
$\therefore x=\frac{2D\lambda }{a}$.....(3)

where D is the distance of the screen from the slit.