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 then equal to the width of the slit if D equals

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

Answer 1

Answer: (B)

$\frac{d^2}{2\lambda }$

In diffraction, fringe width, $\beta =\frac{\lambda D}{d}$
when $\frac{d}{2}=\beta$, then
$\frac{d}{2}=\frac{\lambda D}{d}\Rightarrow D=\frac{d^2}{2\lambda }$.