Question

Two waves having intensities in the ratio of 9 : 1 produce interference. The ratio of maximum to minimum intensity is equal to

• A. 10 : 8
• B. 9 : I
• C. 4 : 1
• D. 2 : l

Answer 1

Answer: (C)

$\frac{I_1}{I_2}=\frac{a_1^2}{a_2^2}=\frac{9}{1}$
$\Rightarrow \frac{a_1}{a_2}=\sqrt{\frac{9}{1}}$
$\Rightarrow \frac{a_1}{a_2}=\frac{3}{1}$
$\therefore \frac{I_{max}}{I_{min}}=\frac{(a_1+a_2{)}^2}{(a_1-a_2{)}^2}$
$=\frac{(3+1{)}^2}{(3-1{)}^2}$
$=\frac{(3{)}^2}{(2{)}^2}=\frac{16}{4}$
$=\frac{4}{1}$
Thus, $I_{max}:I_{min}=4:1$