Question

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

• A. $1.3\text{nm}$
• B. $2.6\text{nm}$
• C. $1.3\mu \text{m}$
• D. $2.6\mu \text{m}$

Answer 1

The correct option is C $1.3\mu \text{m}$

Given:
$\lambda =6500\mathring{A};\theta =30°$

In single slit diffraction for first minima,

$\sin \theta =\frac{\lambda }{a}$

$\sin {30}^{\circ }=\frac{6500\times {10}^{-10}}{a}$

$\frac{1}{2}=\frac{6500\times {10}^{-10}}{a}$

$a=2\times {650010}^{-10}\text{m}$

$\therefore a=1.3\times {10}^{-6}\text{m}=1.3\mu \text{m}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.