Question

In Young's double slit experiment, the ratio of intensities of bright and dark bands is $16$ which means

• A. The ratio of their amplitudes is $5$
• B. Intensities of individual sources are $25$ and $9$ units respectively
• C. The ratio of their amplitudes is $4$
• D. Intensities of individual sources are $4$ and $3$ units respectively

Answer 1

The correct option is B Intensities of individual sources are $25$ and $9$ units respectively

Let the intensities of individual sources be $I_1$ and $I_2$.

Maximum intensity $I_{max}=(\sqrt{I_1}+\sqrt{I_2}{)}^2$

Minimum intensity $I_{min}=(\sqrt{I_1}-\sqrt{I_2}{)}^2$

But $\frac{I_{max}}{I_{min}}=16$

$\therefore$ $\frac{(\sqrt{I_1}+\sqrt{I_2}{)}^2}{(\sqrt{I_1}-\sqrt{I_2}{)}^2}=16$

Or $\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}=4$

Or $5\sqrt{I_1}=3\sqrt{I_2}$

$⟹$ $\frac{I_1}{I_2}=\frac{9}{25}$

Thus intensities of individual sources can be $25$ and $9$ units respectively.