Question

Two slits in Young's double-slit experiment have widths in the ratio 9 : 4.Find the ratio of light intensities at maxima and minima in the interference pattern:

• A. 25:16
• B. 25:1
• C. 5:1
• D. 5:16

Answer 1

The correct option is B 25:1

Given,

$\frac{I_1}{I_2}=\frac{W_1}{W_2}=\frac{9}{4}$

We know that Width is directly proportional to intensity

Therefore,

$\frac{I_{max}}{I_{min}}=\frac{{(\sqrt{I_2}+\sqrt{I_1})}^2}{{(\sqrt{I_2}-\sqrt{I_1})}^2}={\left[\frac{\sqrt{\frac{I_2}{I_1}}+1}{\sqrt{\frac{I_2}{I_1}}-1}\right]}^2$

Substitute all value in above equation

$\frac{I_{max}}{I_{min}}={\left[\frac{\sqrt{\frac{4}{9}}+1}{\sqrt{\frac{4}{9}}-1}\right]}^2={\left[\frac{2+3}{2-3}\right]}^2={\left[\frac{5}{-1}\right]}^2=\frac{25}{1}=25:1$

Option B is correct option