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)

$I=4 I_{0} \cos ^{2}\left(\frac{\phi}{2}\right)$
$=4 I_{0} \cos ^{2}\left(\frac{\pi \Delta}{\lambda}\right)$
$\left\{\because=\frac{2 \pi}{\lambda} \Delta\right\}$
$\Rightarrow \frac{I_{1}}{I_{2}}=\frac{\cos ^{2}\left(\frac{\pi \Delta_{1}}{\lambda}\right)}{\cos ^{2}\left(\frac{\pi\Delta_{2}}{\lambda} \right)}=\frac{\cos ^{2}\left(\frac{\pi \cdot \frac{\lambda}{4}}{\lambda}\right)}{\cos ^{2} \Delta}$
$\frac{I_{1}}{I_{2}}=\frac{1}{2}$