Question

v) In Young's double slit experiment, the
two coherent sources have different
intensities. If the ratio of maximum
intensity to the minimum intensity in the
interference pattern produced is 25:1.
What was the ratio of intensities of the
two sources?
(A) 5:1 (B) 25:1 (C) 3:2 (D) 9:4​

Answer 1

Answer:

9:4

Explanation:

Imax/Imin = (a1+a2)²/(a1-a2)²

Imax/Imin = 25/1

25/1 = (a1+a2)²/(a1-a2)²

Taking square root on both the side

5/1 = a1+a2/a1-a2

a1+a2 = 5 a1-a2 = 1

a1 = 3 a2 = 2

I1/I2 = 3²/2²

I1/I2 = 9/4

= 9:4

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Answer 2

Given,
Maximum intensity to minimum intensity ratio 25:1

To Find,
Ratio of intensities of the source.

Solution,
We know that ,

Imax/I min = (a1+a2)²/(a1-a2)²

Imax/I min = 25/1

⇒25/1 = (a1+a2)²/(a1-a2)²

Taking square root on both the side

⇒5/1 = a1+a2/a1-a2

⇒So, a1+a2 = 5 ,

        a1-a2 = 1

By using two equations,

  a1 = 3 a2 = 2

⇒I1 /I2 = 3²/2²

⇒I1/I2 = 9/4

           = 9:4

Hence, ratio of intensities is 9:4