Question

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

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

Answer 1

The correct option is C $4:1$

$\frac{l_1}{l_2}=\frac{a_1}{a_2}=\frac{9}{1}$

$\frac{a_1}{a_2}=\sqrt{\frac{9}{1}}$

$\frac{a_1}{a_2}=\frac{3}{1}$

$\frac{l_{max}}{l_{min}}=\frac{(a_1+a_2{)}^2}{(a_1-a_2{)}^2}=\frac{(3+1{)}^2}{(3-1{)}^2}$

$=\frac{(4{)}^2}{(2{)}^2}=\frac{16}{4}=\frac{4}{1}$

$l_{,max}:\_min=4:1$