Question

Two coherent light sources of intensity ratio n are employed in an inteference experiment. The ratio of the intensities of the maxima and minima in the inteference pattern is

• A. $\left(\frac{n+1}{n-1}\right)$
  
• B. ${\left(\frac{n+1}{n-1}\right)}^2$
  
• C. $\left(\frac{\sqrt{n}+1}{\sqrt{n}-1}\right)$
  
• D. ${\left(\frac{\sqrt{n}+1}{\sqrt{n}-1}\right)}^2$

Answer 1

The correct option is D

${\left(\frac{\sqrt{n}+1}{\sqrt{n}-1}\right)}^2$

Given $\frac{I_1}{I_2}=n.$ Therefore, the amplitude ratio is
$\frac{A_1}{A_2}=\sqrt{n}$
Now $I_{max}(A_1+A_2{)}^{2}and{I}_{min}=(A_1-A_2{)}^2\therefore \frac{I_{max}}{I_{min}}=\frac{(A_1+A_2{)}^2}{(A_1-A_2{)}^2}=\frac{{(\frac{A_1}{A_2}+1)}^2}{{(\frac{A_1}{A_2}-1)}^2}=\frac{(\sqrt{n}+1{)}^2}{(\sqrt{n}-1{)}^2}$