Question

In Young's double silt experiment, two slits are d distance apart. The interference pattern is observed on a screen at a distance D from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light is ______.

Options

• `d^2/D`

• `d^2/(2D)`

• `D^2/(2d)`

• `D^2/d`

Answer 1

In Young's double silt experiment, two slits are d distance apart. The interference pattern is observed on a screen at a distance D from the slits. The first dark fringe is observed on the screen directly opposite one of the slits. The wavelength of light is `underlinebb(d^2/D)`.

Explanation:

According to the question,

Position of first dark fringe = d/2

For the nth dark fringe, `x_n = (2n - 1)(Dlambda)/(2d)`

Here, n = 1

∴ x₁ = d/2

`(2 xx 1 - 1)(Dlambda)/(2d) = d/2 ⇒ lambda = d^2/D`