If the ratio of maximum to minimum resultant intensity in interference pattern of two waves is 25 : 4, then, ratio of amplitudes two waves is :
Answer & explanation
Correct answer: option 3
The correct answer is option (3) : $7 : 3$
$\frac{I_{max}}{I_{min}}=\frac{(\sqrt{l_1}+\sqrt{l_2})^2}{(\sqrt{l_1}-\sqrt{l_2})^2}$
$\frac{25}{4}=\left(\frac{\sqrt{l_1}+\sqrt{l_2}}{\sqrt{l_1}-\sqrt{l_2}}\right)^2$
$\frac{5}{2}=\left(\frac{\sqrt{l_1}+\sqrt{l_2}}{\sqrt{l_1}-\sqrt{l_2}}\right)$
$3\sqrt{l_1}=7\sqrt{l_2}⇒\frac{l_1}{l_2}=\frac{49}{9}$
$I∝A^2$
$⇒A ∝\sqrt{l}$
$⇒\frac{A_1}{A_2}=\sqrt{\frac{l_1}{l_2}}=\sqrt{\frac{49}{9}}=\frac{7}{3}$