Question

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

A
4 : 1
B
9 : 1
C
2 : 1
D
10 : 8

Solution

## The correct option is B 4 : 1Let the intensity of the two waves be $$I_1$$  and  $$I_2$$Given:    $$I_2 : I_1 = 9 : 1 \implies I_2 = 9 I_1$$Now       $$\dfrac{I_{max}}{I_{min}} = \dfrac{(\sqrt{I_1} + \sqrt{I_2})^2}{(\sqrt{I_2} - \sqrt{I_1})^2} = \dfrac{(\sqrt{I_1} + \sqrt{9 I_1})^2}{(\sqrt{9 I_1} - \sqrt{I_1})^2} = \dfrac{16 I_1}{4 I_1}$$ $$\implies I_{max} : I_{min} = 4 : 1$$Physics

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