Question

At two points P and Q on a screen in Young's double slit experiment, waves from slits $S_1$ and $S_2$ have a path difference of 0 and $\frac{\lambda }{4}$ respectively. The ratio of intensities at P and Q will be :

• A. 2 : 1
• B. $\sqrt{2}:1$
• C. 4 : 1
• D. 3 : 2

Answer 1

Answer: (A)

$\Delta x_1=0$
$\Delta \varphi =0^{\circ }$
$I_1=I_0+I_0+2I_{0}cos{0}^{\circ }=4I_0$
$\Delta x_2=\frac{\lambda }{4}$
$\Delta \theta =\frac{2\pi }{\lambda }.\frac{\lambda }{4}=\left(\frac{\pi }{2}\right)$
$I_2=I_0+I_0+2I_{0}cos\frac{\pi }{2}=2I_0$
$\frac{I_1}{I_2}=\frac{4I_0}{2I_0}=\frac{2}{1}.$