Question

In Young's double slit experiment, for wavelength λ₁ the n^th bright fringe is obtained at a point P on the screen. Keeping the same setting, source of light is replaced by wavelength λ₂ and now (n + 1)^th bright fringe is obtained at the same point P on the screen. The value of n is ______.

Options

• `lambda_1/(lambda_1-lambda_2)`

• `lambda_2/(lambda_1-lambda_2)`

• `(lambda_1-lambda_2)/lambda_2`

• `(lambda_1-lambda_2)/lambda_1`

Answer 1

In Young's double slit experiment, for wavelength λ₁ the n^th bright fringe is obtained at a point P on the screen. Keeping the same setting, source of light is replaced by wavelength λ₂ and now (n + 1)^th bright fringe is obtained at the same point P on the screen. The value of n is `underline(lambda_2/(lambda_1-lambda_2))`.

Explanation:

`beta=(dlambda)/D`

`("nd"lambda_1)/D=(("n"+1)dlambda_2)/D`

nλ₁ = (n + 1)λ₂

`("n"+1)/"n"=lambda_1/lambda_2`

`1/"n"=lambda_1/lambda_2-1=(lambda_1-lambda_2)/lambda_2`

`"n"=lambda_2/(lambda_1-lambda_2)`