Question

Two coherent sources of light interfere. The intensity ratio of two sources is $1:4$. For this interference pattern if the value of $\frac{I_{\max }+I_{\min }}{I_{\max }-I_{\min }}$ is equal to $\frac{2\alpha +1}{\beta +3}$, then $\frac{\alpha }{\beta }$ will be :

• A. $1.5$
• B. 2
• C. $0.5$
• D. 1

Answer 1

Answer: (B)

$\frac{I_1}{I_2}=\frac{1}{4}$
$I_2=4I_1$
$I_{\max }=I_1+4I_1+2\sqrt{I_{1}4I_1}=9I_1$
$I_{\min }=I_1+4I_1-2\sqrt{I_{1}4I_1}=I_1$
$\therefore \frac{9I_1+I_1}{9I_1-I_1}=\frac{10}{8}=\frac{5}{4}=\frac{2\alpha +1}{\beta +1}$
$\alpha =2\beta =1$
$\therefore \frac{\alpha }{\beta }=\frac{2}{1}=2$