Question

The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio `("I"_"max" - "I"_"min")/("I"_"max" + "I"_"min")` will be ______

Options

• `(2sqrt"n")/("n" + 1)^2`

• `sqrt"n"/("n" + 1)`

• `(2sqrt"n")/("n" + 1)`

• `sqrt"n"/("n" + 1)^2`

Answer 1

The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio `("I"_"max" - "I"_"min")/("I"_"max" + "I"_"min")` will be `underline((2sqrt"n")/("n" + 1))`.

Explanation:

Given,

`"I"_1/"I"_2 = "n"`

∴ I₁ = nI₂

∴ `"I"_"max" = (sqrt"I"_1 + sqrt"I"_2)^2 = (sqrt"nI"_2 + sqrt"I"_2)^2`

Say I₂ = I 

∴ `"I"_"max" = (sqrt"n" + 1)^2"I"`

Similarly, `"I"_"min" = (sqrt"n" - 1)^2"I"`

∴ `("I"_"max" - "I"_"min")/("I"_"max" + "I"_"min") = ((sqrt"n" + 1)^2 - (sqrt"n" - 1)^2)/((sqrt"n" + 1)^2 + (sqrt"n" - 1)^2)`

= `("n" + 1 + 2sqrt"n" - "n" - 1 + 2sqrt"n")/("n" + 1 + 2sqrt"n" + "n" + 1 - 2sqrt"n")`

= `(4sqrt"n")/(2"n" + 2) = (2sqrt"n")/("n" + 1)`