Question

The path difference between two interfering waves of equal intensities at a point on the screen is $\lambda /4.$ The ratio of intensity at this point and that at the central fringe will be

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 1 : 4

Answer 1

Answer: (B)

$I=4I_0{\cos }^2\left(\frac{\varphi }{2}\right)$
$=4I_0{\cos }^2\left(\frac{\pi \Delta }{\lambda }\right)$
$\left\{\because =\frac{2\pi }{\lambda }\Delta \right\}$
$\Rightarrow \frac{I_1}{I_2}=\frac{{\cos }^2\left(\frac{\pi {\Delta }_1}{\lambda }\right)}{{\cos }^2\left(\frac{\pi {\Delta }_2}{\lambda }\right)}=\frac{{\cos }^2\left(\frac{\pi \cdot \frac{\lambda }{4}}{\lambda }\right)}{{\cos }^2\Delta }$
$\frac{I_1}{I_2}=\frac{1}{2}$