Q. A slit of width $a$ is illuminated by white light. For red light $(\lambda = 6500\ \mathring{\mathrm{A}})$, the first minima is obtained at $\theta = 30{^\circ}$. Then the value of $a$ will be
A) $3250\ \mathring{\mathrm{A}}$
B) $6.5 \times 10^{- 4}mm$
C) $1.24\ microns$
D) $2.6 \times 10^{- 4}cm$
Explanation
(c) For first minima $\theta = \frac{\lambda}{a}$ or $a = \frac{\lambda}{\theta}$
$\therefore a = \frac{6500 \times 10^{- 8} \times 6}{\pi}\ \left( As\ 30{^\circ} = \frac{\pi}{6}radian \right)$
$= 1.24 \times 10^{- 4}cm = 1.24$ microns
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.