Question

The interference pattern with two coherent light sources of density ratio $n$. In the interference pattern, the ratio $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ will be:

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

Answer 1

The correct option is B $\frac{2\sqrt{n}}{n+1}$

Given that $\frac{I_1}{I_2}=n{I}_{max}=I_1+I_2+2\sqrt{I_1{I}_2}{I}_{min}=I_1+I_2-2\sqrt{I_1{I}_2}\therefore \frac{I_{max}+I_{min}}{I_{max}-I_{min}}=\frac{4\sqrt{I_1{I}_2}}{2\sqrt{I_1{I}_2}}=\frac{4I_2\sqrt{I_1/I_2}}{2I_2\sqrt{I_1/I_2+1}}=\frac{2\sqrt{n}}{n+1}$