Question

Two coherent sources of intensity ratio '$\alpha$' interfere. In interference pattern $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=$

• A. $\frac{2\alpha }{1+\alpha }$
• B. $\frac{2\sqrt{\alpha }}{1+\alpha }$
• C. $\frac{2\alpha }{1+\sqrt{\alpha }}$
• D. $\frac{1+\alpha }{2\alpha }$

Answer 1

Answer: (B)

$\frac{2\sqrt{\alpha }}{1+\alpha }$

We have:

$I_{max}={(\sqrt{I_1}+\sqrt{I_2})}^2{I}_{min}={(\sqrt{I_1}-\sqrt{I_2})}^2{I}_1={\alpha I}_2\Rightarrow \frac{I_{max}-I_{min}}{I_{max}{+I}_{min}}=\frac{4\sqrt{I_1{I}_2}}{2(I_1+I_2)}=\frac{4\sqrt{\alpha }{I}_2}{2(1+{\alpha )I}_2}=\frac{2\sqrt{\alpha }}{1+\alpha }$