Question

The ratio of intensities in consecutive maxima in a diffraction pattern due to a single slit is

• A. $1:2:3$
• B. $1:4:9$
• C. $1:\frac{2}{\pi ^{2}}:\frac{3}{\pi ^{2}}$
• D. $1:\frac{4}{9 \pi ^{2}}:\frac{4}{25 \pi ^{2}}$

Answer 1

Answer: (D)

$I=I_{0}\left(\frac{sin \left(\alpha \right)}{\alpha }\right)^{2}$ and $\alpha =0,\frac{3 \pi }{2},\frac{5 \pi }{2}, \, \ldots \ldots \ldots $ , for maxima
The ratio of Intensities of successive maxima is
$1:\left(\frac{2}{3 \pi }\right)^{2}:\left(\frac{2}{5 \pi }\right)^{2}$ or $1:\frac{4}{9 \pi ^{2}}:\frac{4}{25 \pi ^{2}}$