Question

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

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

Answer 1

Answer: (A)

$\frac{I_1}{I_2}=\frac{a^2}{b^2}=β∴\frac{a}{b}=\sqrt{β}$
Fringe visibility is given by
$V=\frac{I_{max}−I_{min}}{I_{max}+I_{min}}=\frac{{\left(a+b\right)}^2−{\left(a−b\right)}^2}{{\left(a+b\right)}^2+{\left(a−b\right)}^2}$
$=\frac{4ab}{2\left(a^2+b^2\right)}=\frac{2\left(a/b\right)}{\left(\frac{a^2}{b^2}+1\right)}=\frac{2\sqrt{β}}{β+1}$