Question

When the frequency of the light used is changed from 4 × 10$^14$ s$^-1 $to 5 × 10$^14$ 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. $1.5\times10^{-7}m$
• B. $3\times10^{-7}m$
• C. $5\times10^{-7}m$
• D. $6\times10^{-7}m$

Answer 1

Answer: (C)

$\theta =\frac{2\lambda}{d} or, \Delta\theta =\frac{2\Delta\lambda}{d} or, d=\frac{2\Delta\lambda}{\Delta\theta}$
$\Delta\lambda=\frac{3\times10^{8}}{4\times10^{14}}-\frac{3\times10^{8}}{5\times10^{14}} =10^{6} \left(0.75-0.6\right)=0.15\times10^{-6} =1.5\times10^{-7}$
$d=\frac{2\times1.5\times10^{-7}}{0.6}=\frac{2\times15\times10^{-7}}{6} =5\times10^{-7}$