Question

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

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

Answer 1

The correct option is C $1.3\text{micron}$

For first minimum, $a\sin \theta =1\times \lambda$

$a=\frac{\lambda }{\sin \theta }=\frac{6.5\times {10}^{-7}}{\sin {30}^{\circ }}$

$=13\times {10}^{-7}\text{m}=1.3\text{micron}$

Hence, $\left(C\right)$ is the correct answer.