Question

A slit of width a is illuminated by white light. The first minimum for red light $\left(\lambda = 6500 \mathring{A} \right) $ will fall at $\theta = 30^{\circ}$ when $a$ will be

• A. $3200 \mathring{A} $
• B. $6.5 \times 10^{-4}\, mm$
• C. $1.3$ micron
• D. $2.6 \times 10^{-4}\, cm$

Answer 1

Answer: (C)

For first minimum, $a\, sin\theta = 1\lambda$
$a = \frac{\lambda}{sin\,\theta} = \frac{6.5 \times 10^{-7}}{sin\,30^{\circ}}$
$ = 13 \times 10^{-7} $
$ = 1.3 $ micron