Question

Ratio of intensity of two waves is 25 : 1. If
interference occurs, then ratio of maximum and
minimum intensity should be:
(1) 25: 1
(2) 5:1
(3) 9:4
(4)4:9​

Answer 1

Answer:

$\dfrac{I_{max}}{I_{min}}=\dfrac{9}{4}$

Explanation:

Let $I_1\ and\ I_2$ are intensities of two waves. When two waves superimpose on each other, interference pattern is formed.

Given that, $\dfrac{I_1}{I_2}=\dfrac{25}{1}$

The maximum intensity is given by :

$I_{max}=(\sqrt{I_1} +\sqrt{I_2})^2$................(1)

The minimum intensity is given by :

$I_{min}=(\sqrt{I_1} -\sqrt{I_2})^2$...........(2)

Dividing equation (1) and (2) we get :

$\dfrac{I_{max}}{I_{min}}=\dfrac{(\sqrt{I_1} +\sqrt{I_2})^2}{(\sqrt{I_1} -\sqrt{I_2})^2}$

$\dfrac{I_{max}}{I_{min}}=\dfrac{(5 +1)^2}{(5 -1)^2}$

$\dfrac{I_{max}}{I_{min}}=\dfrac{9}{4}$

So, the ratio of maximum and minimum intensity should be 9:4.

Learn more :

Topic : Interference

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