Question

In an interference pattern the ratio of the intensity of light at the bright fringe to that at the dark fringe is $9:1$. Then the ratio of the amplitudes of the two interfering waves:

• A. $3:1$
• B. $2:1$
• C. $1:4$
• D. $5:4$

Answer 1

Answer: (B)

$2:1$

$\frac{I_{max}}{I_{min}}=\frac{9}{1}$

As $I\propto a^2$

$\frac{a_{max}}{a_{min}}=\frac{3}{1}=\frac{a_1+a_2}{a_1-a_2}$

$\Rightarrow 3a_1-3a_2=a_1+a_2$

$\Rightarrow 2a_1=4a_2$ or $a_1=2a_2$
$\Rightarrow \frac{a_1}{a_2}=2$