Question

Light of wavelength $\lambda$ is incident on a slit of width $d$, the resulting diffraction pattern is observed on a screen at a distance $D$. The linear width of the principal maximum is equal to the width of the slit, if $D$ equal to

• A. $\frac{d^{2}}{2 \lambda}$
• B. $\frac{d}{\lambda}$
• C. $\frac{2 \lambda^{2}}{d}$
• D. $\frac{2 \lambda}{d}$

Answer 1

Answer: (A)

Linear width of central maximum
$\beta_{0}=\frac{2 \lambda D}{d}$
Given $\beta_{0}=d$,
$\therefore d =\frac{2 \lambda D}{d} $
$d^{2} =2 \lambda D $
$D =\frac{d^{2}}{2 \lambda}$