Question

The ratio of the intensity of two light waves is 16.9. The ratio of maximum and minimum intensity in their interference pattern will be

(1) 25:7
(2) 49:1
(3) 4:3
(4) 256:81
​

Answer 1

The answer is (2) 49:1

Answer 2

Given info : The ratio of the intensity of two light waves is 16 : 9.

To find : The ratio of maximum and minimum intensity in their interference pattern will be..

solution : intensity is given by, I = I₁ + I₂ + 2√I₁I₂ cosΦ

for maximum intensity, Φ = 0°

then, I = (√I₁ + √I₂)²

and for minimum intensity, Φ = 180°

then, I = (√I₁ - √I₂)²

now the ratio of maximum to minimum intensity = (√I₁ + √I₂)²/(√I₁ - √I₂)²

= (√(I₁/I₂) + 1)²/(√(I₁/I₂ - 1)²

given, I₁/I₂ = 16/9

so, Ratio of maximum to minimum intensity = (√(16/9) + 1)²/(√(16/9) - 1)²

= (4/3 + 1)²/(4/3 - 1)²

= (4 + 3)/(4 - 3)²

= 7²/1²

= 49/1

Therefore the ratio of maximum to minimum intensity in their interference patterns is 49 : 1.

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