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)

$\Delta x_{1} = 0$
$\Delta\phi = 0^{\circ}$
$I_{1} = I_{0} + I_{0} + 2I_{0} \,cos0^{\circ} = 4I_{0}$
$\Delta x_{2} = \frac{\lambda}{4}$
$\Delta\theta = \frac{2\pi}{\lambda}. \frac{\lambda}{4} = \left(\frac{\pi}{2}\right)$
$I_{2} = I_{0} + I_{0} + 2I_{0} \,cos \frac{\pi}{2} = 2I_{0}$
$\frac{I_{1}}{I_{2}} = \frac{4I_{0}}{2I_{0}} = \frac{2}{1}.$