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

Answer 1

Answer: (B)

Intensities of individual source are 25 and 9 units respectively.

Let the intensities of individual source be $I_1$ and $I_2$ having amplitude $A_1$ and $A_2$ respectively.

Bright fringe (maximum) intensity, $I_{max}=(\sqrt{I_1}+\sqrt{I_2}{)}^2$

Darkt fringe (minimum) intensity, $I_{min}=(\sqrt{I_1}-\sqrt{I_2}{)}^2$

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

$\frac{(\sqrt{I_1}+\sqrt{I_2})}{(\sqrt{I_1}-\sqrt{I_2})}=4$$⟹\frac{\sqrt{I_1}}{\sqrt{I_2}}=\frac{5}{3}$

$\therefore$ $I_2=9$ units $⟹I_1=25$ units

Also, amplitude $A\propto \sqrt{I}$

$⟹$ Ratio of amplitude $\frac{A_1}{A_2}=\frac{\sqrt{I_1}}{\sqrt{I_2}}=\frac{5}{3}$