Question

The interference pattern is obtained with two

coherent light sources of intensity ratio n. In

the interference pattern, the ratio I I

I I

max min

max min

–



will

be :​

Answer 1

QUESTION:

• The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference patten, the ratio

I max - I min / I max + I min will be

SOLUTION:

I 1 / I 2 = n / 1 (given)

I max = ( √ I 1 + √ I 2 )²

I max = (√n +1)²

I min = ( √ I 1 - √ I 2 )²

I min = (√n - 1)²

I max - I min / I max + I min

$= \frac{ {( \sqrt{n} + 1) }^{2} -{( \sqrt{n} - 1) }^{2} }{ \:{( \sqrt{n} + 1) }^{2} +{( \sqrt{n} - 1) }^{2}}$

$= \frac{n + 1 + 2 \sqrt{n } - n - 1 + 2 \sqrt{n} }{n + 1 + 2 \sqrt{n} + n + 1 - 2 \sqrt{n} }$

$= \frac{4 \sqrt{n} }{2n + 2}$

$= \frac{2 \sqrt{n} }{n + 1}$

$\boxed{ \frac{i \: max - i \: min}{i \: max + i \: min} = \frac{2 \sqrt{2} }{n + 1} }$