Question

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

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

Answer 1

The correct option is A $\frac{d^2}{2\lambda }$

Position of first minima above the central maxima $y=\frac{\lambda D}{d}$
So, linear width of the central maxima $=2y=\frac{2\lambda D}{d}$
Given : $2y=d$
where $d$ is the width of slit.
$\therefore$ $\frac{2\lambda D}{d}=d$
$⟹D=\frac{d^2}{2\lambda }$