Question

In a Young's double slit experiment, the intensity at the central maximum is $I_0$. The intensity at a distance $\beta /4$ from the central maximum is ($\beta$ is fringe width )

• A. $I_0$
• B. $\frac{I_0}{2}$
• C. $\frac{I_0}{\sqrt{2}}$
• D. $\frac{I_0}{4}$

Answer 1

The correct option is B $\frac{I_0}{2}$

Central max intensity $=I_0$

$\begin{array}{c}\beta =\frac{\lambda D}{d}\\ Y=\frac{\lambda D}{4d}\\ \Delta x=\frac{Yd}{D}\Rightarrow \Delta x=\frac{\lambda Dd}{4dD}=\frac{\lambda }{4}\\ \varnothing =\frac{2\pi }{\lambda }\times \frac{\lambda }{4}=\frac{\pi }{2}\\ I=I_1+I_2+2\sqrt{I_1{I}_2\cos \varnothing }\\ \varnothing =0,I=I_0,I_1=I_2=I_s\\ I_0=4I_s\to \left(i\right)\\ nowlos\varnothing =\frac{\pi }{2}\\ \Rightarrow I=2I_s\to \left(ii\right)\\ \therefore from\left(i\right)+\left(ii\right),\\ I=\frac{I_0}{2}\end{array}$