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. 2:01
• B. $\sqrt{2} : 1$
• C. 4:01
• D. 3:02

Answer 1

Answer: (A)

2:01

Answer 2

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