Question

If the ratio of the intensity of two coherent sources is $4$. The ratio $\left[\frac{I_{max}-I_{min}}{I_{max}+I_{min}}\right]$ is equal to,

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

Answer 1

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

For interference of light,

$I_{max}=(\sqrt{I_1}+\sqrt{I_2}{)}^2$

And, $I_{min}=(\sqrt{I_1}-\sqrt{I_2}{)}^2$


$\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=\frac{(\sqrt{I_1}+\sqrt{I_2}{)}^2-(\sqrt{I_1}-\sqrt{I_2}{)}^2}{(\sqrt{I_1}+\sqrt{I_2}{)}^2+(\sqrt{I_1}-\sqrt{I_2}{)}^2}$

$=\frac{{(\sqrt{\frac{I_1}{I_2}}+1)}^2-{(\sqrt{\frac{I_1}{I_2}}-1)}^2}{{(\sqrt{\frac{I_1}{I_2}}+1)}^2+{(\sqrt{\frac{I_1}{I_2}}-1)}^2}$

As, $\frac{I_1}{I_2}=4$

$\frac{I_{max}-I_{min}}{I_{max}+I_{min}}=\frac{(2+1{)}^2-(2-1{)}^2}{(2+1{)}^2+(2-1{)}^2}$

$=\frac{8}{10}=\frac{4}{5}$

Hence, $\left(B\right)$ is the correct answer.