Question

Let $S_1$ and $S_2$ be the two slits in Young's double-slit experiment. If central maxima is observed at $P$ and angle $\angle S_{1}P{S}_2=\theta$, then the fringe width for the light of wavelength $\lambda$ will be (assume $\theta$ to be a small angle)

• A. $\lambda /\theta$
• B. $\lambda \theta$
• C. $2\lambda /\theta$
• D. $\lambda /2\theta$

Answer 1

The correct option is A $\lambda /\theta$

As shown in figure

For small angle $\cos \frac{\theta }{2}\cong \frac{\theta }{2}=\frac{d}{2D}$

$\theta =\frac{\lambda d}{\lambda D}=\frac{\lambda }{\beta }\Rightarrow \beta =\frac{\lambda }{\theta }$