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=4 I _1 $
$ I _{\max }= I _1+4 I _1+2 \sqrt{ I _1 4 I _1}=9 I _1 $
$ I _{\min }= I _1+4 I _1-2 \sqrt{ I _1 4 I _1}= I _1 $
$\therefore \frac{9 I _1+ I _1}{9 I _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$