Question

In the given figure, $C$ is middle point of lines $S_{1}\, S_{2} .$ A monochromatic light of wavelength $\lambda$ is incident on slits. The ratio of intensities of $S_{3}$ and $S_{4}$ is

• A. zero
• B. $\infty$
• C. 4 : 1
• D. 1 : 4

Answer 1

Answer: (B)

Path difference, $\Delta x=S_{1} S_{3}-S_{2} S_{3}=0$
$\therefore \phi=\frac{2 \pi}{\lambda} \Delta x=0$
$\therefore I_{3}=I_{0}+I_{0}+2 \sqrt{I_{0}+I_{0}\left(\cos 0^{\circ}\right)}$
$\therefore I_{3}=4 I_{0}$
The path difference at $S_{4}$ is
$\Delta x '=S_{1} S_{4}-S_{2} S_{4}=\frac{x d}{D}$ (Here, $x=\frac{\lambda D}{2 d}$)
$=\frac{d}{D} \times \frac{\lambda D}{2 d}=\frac{\lambda}{2}$
$\therefore \phi' =\frac{2 \pi}{\lambda} \cdot \frac{\lambda}{2}=\pi$
$ \therefore I_{4} =I_{0}+I_{0}+2 I_{0} \cos \pi=0$
$\therefore $ Ratio $=\frac{I_{3}}{I_{4}}=\frac{4 I_{0}}{0}=\infty$