Question

A slit of width $a$ is illuminated by white light in single slit diffraction. The first minimum for red light $\lambda =6500 \, Å$ will fall at $\theta =30^{o},$ when $a$ is

• A. $3250 \, Å$
• B. $6.5\times 10^{- 4} \, cm$
• C. $1.3 \, \mu m$
• D. $2.6\times 10^{- 4} \, cm$

Answer 1

Answer: (C)

$sin \theta =\frac{\lambda }{a}$
$\Rightarrow sin 30^{o}=\frac{6500}{a}Å$
$\therefore \, \, \frac{1}{2}=\frac{6500}{a}Å$
$\Rightarrow a=2\times 6500 \, Å$
$\Rightarrow a=2\times 6500\times 10^{- 10} \, m$
$\therefore \, \, \Rightarrow \, \, \, a=1.3\times 10^{- 6} \, m$