Question

Consider two coherent, monochromatic (wavelength $\lambda$ ) sources, $S_1$ and $S_2$ , separated by a distance $d$ . The ratio of intensities of $S_1$ and that of $S_2$ (which is responsible for interference at point $P$ , where detector is located) is $4$ . The distance of point $P$ from $S_1$ is (if the resultant intensity at point $P$ is equal to $\frac{9}{4}$ times of intensity of $S_1$ ) (Given: $\angle S_2{S}_{1}P=90^{\circ }$ , $d>0$ and $n$ is a positive integer)

• A. $\frac{d^2-n^2{\lambda }^2}{2n\lambda }$
• B. $\frac{d^2+n^2{\lambda }^2}{2n\lambda }$
• C. $\frac{n\lambda d}{\sqrt{d^2-n^2{\lambda }^2}}$
• D. $\frac{2n\lambda d}{\sqrt{d^2-n^2{\lambda }^2}}$

Answer 1

Answer: (A)

$\frac{9}{4}$ intensity of $S_1=9$ times of intensity $S_2$
Intensity of maxima = ${\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2=9I_2$
$\Rightarrow S_{2}P-S_{1}P=n\lambda$ for maxima
$\sqrt{d^2+x^2}-x=n\lambda x=\frac{d^2-n^2{\lambda }^2}{2n\lambda }$