Question

The intensity ratio for the two interfering beam of light is $\beta$. What is the value of
$\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ ?

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

Answer 1

The correct option is B $\frac{2\sqrt{\beta }}{1+\beta }$

Given $\frac{I_1}{I_2}=\beta$

$I_{max}=I_1+I_2+2\sqrt{I_1{I}_2}$

$I_{min}=I_1+I_2-2\sqrt{I_1{I}_2}$

$\therefore \frac{I_{max}-I_{min}}{I_{max}+I_{min}}=\frac{4\sqrt{I_1{I}_2}}{2(I_1+I_2)}=\frac{2\sqrt{I_2^2\beta }}{I_2(\beta +1)}=\frac{2\sqrt{\beta }}{\beta +1}$