Question

The two coherent sources with intensity ratio $\beta$ produce interference. The fringe visibility will be

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

Answer 1

The Correct Option is A

$\frac{I_{1}}{I_{2}}=\frac{a^{2}}{b^{2}}=\beta \therefore \frac{a}{b}=\sqrt{\beta}$ Fringe visibility is given by $V=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=\frac{\left(a+b\right)^{2}-\left(a-b\right)^{2}}{\left(a+b\right)^{2}+\left(a-b\right)^{2}}$ $=\frac{4ab}{2\left(a^{2}+b^{2}\right)}=\frac{2\left(a/b\right)}{\left(\frac{a^{2}}{b^{2}}+1\right)}=\frac{2\sqrt{\beta}}{\beta+1}$