Q84 / 100 · BITSAT 2023 (Memory Based Paper 1) · Physics
The ratio of intensities at two points $\mathrm{P}$ and $\mathrm{Q}$ on the screen in a Young's double slit experiment where phase difference between two wave of same amplitude are $\frac{\pi}{3}$ and $\frac{\pi}{2}$, respectively are
- A$1: 3$
- B$3: 1$
- Correct answerC$3: 2$
- D$2: 3$
Solution
Intensity at a point in Young's double slit experiment is given by
$\mathrm{I}=\mathrm{I}_1+\mathrm{I}_2+2 \sqrt{\mathrm{I}_1 \mathrm{I}_2} \cos \phi$
Here $\mathrm{I}_1=\mathrm{I}_2=\mathrm{I}_0$ (say)
At $P$
$\therefore \mathrm{I}_{\mathrm{p}}=\mathrm{I}_0+\mathrm{I}_0+2 \mathrm{I}_0 \cos \frac{\pi}{3}=2 \mathrm{I}_0+2 \mathrm{I}_0 \times \frac{1}{2}=3 \mathrm{I}_0$
At $Q$
$\mathrm{I}_{\mathrm{Q}}=\mathrm{I}_0+\mathrm{I}_0+2 \mathrm{I}_0 \cos 90^{\circ}=2 \mathrm{I}_0$
$\frac{\mathrm{I}_{\mathrm{P}}}{\mathrm{I}_{\mathrm{Q}}}=\frac{3}{2}$
$\mathrm{I}=\mathrm{I}_1+\mathrm{I}_2+2 \sqrt{\mathrm{I}_1 \mathrm{I}_2} \cos \phi$
Here $\mathrm{I}_1=\mathrm{I}_2=\mathrm{I}_0$ (say)
At $P$
$\therefore \mathrm{I}_{\mathrm{p}}=\mathrm{I}_0+\mathrm{I}_0+2 \mathrm{I}_0 \cos \frac{\pi}{3}=2 \mathrm{I}_0+2 \mathrm{I}_0 \times \frac{1}{2}=3 \mathrm{I}_0$
At $Q$
$\mathrm{I}_{\mathrm{Q}}=\mathrm{I}_0+\mathrm{I}_0+2 \mathrm{I}_0 \cos 90^{\circ}=2 \mathrm{I}_0$
$\frac{\mathrm{I}_{\mathrm{P}}}{\mathrm{I}_{\mathrm{Q}}}=\frac{3}{2}$
Hence, the correct answer is option: 'C'.