Question

Light of wavelengths $\lambda$ 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 equals

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

Answer 1

The correct option is C

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

If D>>d, the linear width of the central principal maximum =angular width $\times$ distance D=$\frac{2\lambda D}{d},$ where d is the width of the slit. The linear width of the principal maximum will be equal to slit width for a value of D given by
$\frac{2\lambda D}{d}=dorD=\frac{d^2}{2\lambda }$