Question

The ratio of intensities of two waves is $16:9$. If they produce interference, then ratio of maximum and minimum intensities will be

• A. 4 : 3
• B. 49 : 1
• C. 64 : 27
• D. 81 : 49

Answer 1

Answer: (B)

Since, $\frac{I_1}{I_2}=\frac{16}{9}=\frac{a_1^2}{a_2^2}$
$\Rightarrow \frac{a_1}{a_2}=\sqrt{\frac{16}{9}}=\frac{4}{3}$
or $a_1=\frac{4}{3}{a}_2$
$\therefore \frac{I_{max}}{I_{\min }}=\frac{(a_1+a_2{)}^2}{(a_1-a_2{)}^2}$
$=\frac{{\left(\frac{4}{3}{a}_2+a_2\right)}^2}{{\left(\frac{4}{3}{a}_2-a_2\right)}^2}=49:1$