Question

The intensity ratio of maxima and minima in an interference pattern is 4 : 1. Find the ratio of slit widths.

• A. 8:1
• B. 9:1
• C. 16:1
• D. 25:1

Answer 1

Answer: (B)

9:1

Given,

$\frac{I_1}{I_2}=\frac{W_1}{W_2}=\frac{4}{1}$

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

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

Option B is correct option