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Question

Physics Question on Youngs double slit experiment

Interference fringes are obtained using two coherent sources whose intensities are in the ratio 4 : 1. Then the ratio of the intensities of the bright and dark bands is

A

25:09:00

B

4:01

C

5:01

D

9:01

Answer

9:01

Explanation

Solution

ImaxImin=(a1+a2)2(a1−a2)2\frac{I_{max}}{I_{min}}=\frac{(a_1 +a_2 )^2}{(a_1 -a_2)^2} Here a12a22=41i.e.,a1a2=21i.e.,a2=a12∴ IaxImin=(3a12)2×(2a1)2=91Here \,\frac{a_1^2}{a_2^2}=\frac{4}{1}i.e., \frac{a_1}{a_2}=\frac{2}{1}i.e., a_2 =\frac{a_1}{2}\therefore\,\frac{I_{ax}}{I_{min}}=\left(\frac{3a_1}{2}\right)^2 \times \left(\frac{2}{a_1}\right)^2=\frac{9}{1}