Question

In Young's double experiment, in air interference pattern second minimum is observed exactly in front of one slit. The distance between the two coherent source is 'd' and the distance between source and screen is 'D'. The wavelength of light source used is ______.

Options

• `"d"^2/"D"`

• `"d"^2/(2"D")`

• `"d"^2/(3"D")`

• `"d"^2/(4"D")`

Answer 1

In Young's double experiment, in air interference pattern second minimum is observed exactly in front of one slit. The distance between the two coherent source is 'd' and the distance between source and screen is 'D'. The wavelength of light source used is `underlinebb("d"^2/(3"D"))`.

Explanation:

In YDSE, position of a minima

y = `((2"n"-1)lambda"D")/"d"`      ...(i)

Here, y = `"d"/2`, n = 2

Substituting y = `"d"/2` and n = 2 in eq. (i)

`"d"/2="D"/"d"((2xx2-1)/2)`λ

⇒ `"d"/2="D"/"d"3/2`λ

∴ λ = `"d"^2/(3"D")`