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Question: The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sou...

The intensity ratio of the maxima and minima in an interference pattern produced by two coherent source of light is 9:1 The intensities of the used light sources are in ratio:

A

3:1

B

4:1

C

9:1

D

10:1

Answer

4:1

Explanation

Solution

: Imax⁡Imin⁡=(A+B)2(A−B)2\frac{I_{\max}}{I_{\min} = \frac{(A + B)^{2}}{(A - B)^{2}}}

91=(A+B)2(A−B)2\frac{9}{1} = \frac{(A + B)^{2}}{(A - B)^{2}}

Or 31=A+BA−Bor3A−3B=A+B\frac{3}{1} = \frac{A + B}{A - B^{}}or3A - 3B = A + B

Or 2A=4BorA=2B⇒AB=22A = 4BorA = 2B \Rightarrow \frac{A}{B} = 2

∴I1I2=A2B2=41\therefore\frac{I_{1}}{I_{2}} = \frac{A^{2}}{B^{2}} = \frac{4}{1}