Question

If the ratio of intensity of two coherent sources is $4,$ then the visibility $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ of the fringes is

• A. $4$
• B. $\frac{4}{5}$
• C. $\frac{3}{5}$
• D. $9$

Answer 1

The correct option is B $\frac{4}{5}$

Given, visibility$=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$

$\therefore v=\frac{I_1+I_2+2\sqrt{I_1{I}_2}-I_1-I_2+2\sqrt{I_1{I}_2}}{I_1+I_2+2\sqrt{I_1{I}_2}+I_1+I_2-2\sqrt{I_1{I}_2}}$

$\Rightarrow v=\frac{4\sqrt{I_1{I}_2}}{2(I_1+I_2)}$

Given, $\frac{I_1}{I_2}=4\Rightarrow I_1=4I_2$

$\Rightarrow v=\frac{4\sqrt{I_2\times 4I_2}}{2\left(5I_2\right)}=\frac{4}{5}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.