Question

The ratio of the amplitude of the two sources producing interference $3:5$, the ratio of intensities at maxima and minima is

• A. $25:6$
• B. $5:3$
• C. $16:1$
• D. $25:9$

Answer 1

The correct option is C

$16:1$

Step 1: Compute the ratio of amplitudes

Given: Ratios of the amplitude is $3:5$.

$A_{max}=3+5$

$A_{max}=8$

$A_{min}=5-3$

$A_{max}=2$

Now, the ratio of $A_{max}$ and $A_{min}$,

$\frac{A_{max}}{A_{min}}=\frac{8}{2}$

$\frac{A_{max}}{A_{min}}=\frac{4}{1}$

Step 2: Find the ratio of intensities at maxima and minima
Since intensity is directly proportional to the square of the amplitude.

Therefore, $\frac{{\mathrm{I}}_{\max }}{{\mathrm{I}}_{\min }}={\left(\frac{4}{1}\right)}^2$

$\frac{{\mathrm{I}}_{\max }}{{\mathrm{I}}_{\min }}=\frac{16}{1}$

Hence option $\left(C\right)$ is the correct option.