Question

When the frequency of the light used is changed from 4 × 10${}^{1}4$ s${}^{-}1$to 5 × 10${}^{1}4$ s${}^{-}1,$ then angular width of the principal (central) maximum in a single slit Fraunhoffer diffraction pattern changes by 0.6 radian. What is the width of the slit (assume that the experiment is performed in vacuum)?

• A. $1.5\times 10^{-7}m$
• B. $3\times 10^{-7}m$
• C. $5\times 10^{-7}m$
• D. $6\times 10^{-7}m$

Answer 1

Answer: (C)

$\theta =\frac{2\lambda }{d}or,\Delta \theta =\frac{2\Delta \lambda }{d}or,d=\frac{2\Delta \lambda }{\Delta \theta }$
$\Delta \lambda =\frac{3\times 10^8}{4\times 10^{14}}-\frac{3\times 10^8}{5\times 10^{14}}=10^6\left(0.75-0.6\right)=0.15\times 10^{-6}=1.5\times 10^{-7}$
$d=\frac{2\times 1.5\times 10^{-7}}{0.6}=\frac{2\times 15\times 10^{-7}}{6}=5\times 10^{-7}$