Question

The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio `("I"_"max" - "I"_"min")/("I"_"max" + "I"_"min")` is `5/x`. Then the value of x will be equal to ______.

Options

• 3

• 4

• 2

• 1

Answer 1

The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio `("I"_"max" - "I"_"min")/("I"_"max" + "I"_"min")` is `5/x`. Then the value of x will be equal to 4.

Explanation:

We have

`("I"_"max")/("I"_"min") = (sqrt"I"_1+sqrt"I"_2)^2/(sqrt"I"_1-sqrt"I"_2)^2`

= `(sqrt4+sqrt1)^2/(sqrt4-sqrt1)^2`

= `9/1`

By componendo and dividendo

`("I"_"max" + "I"_"min")/("I"_"max" - "I"_"min")=(9+1)/(9-1)`

= `10/8=5/4`

So, x = 4