Question

In Young's double slit experiment, the ratio of intensities of bright and dark frings is $9$. This means that

• A. the intensities of individual source are $5$ and $4$ units respectively
• B. the intensities of individual source are $4$ and $1$ units respectively
• C. the ratio of their amplitude is $3$
• D. the ratio of their amplitude is $4$

Answer 1

The correct option is B the intensities of individual source are $4$ and $1$ units respectively

$\frac{I_{max}}{I_{min}}=\frac{{(\sqrt{I_1}+\sqrt{I_2})}^2}{{(\sqrt{I_1}-\sqrt{I_2})}^2}=\frac{9}{1}$

$\frac{(\sqrt{I_1}+\sqrt{I_2})}{(\sqrt{I_1}-\sqrt{I_2})}=\frac{3}{1}$

$\sqrt{\frac{I_1}{I_2}}=\frac{2}{1}$

$\frac{I_1}{I_2}=\frac{4}{1}$

So, the ratios of their intensities is $4:1$