Question

In Young's double slit experiment fifth dark fringe is formed opposite to one of the slits. If D is the distance between the slits and the screen and d is the separation between the slits, then the wavelength of light used is ______.

Options

• `"d"^2/(5"D")`

• `"d"^2/(9"D")`

• `"d"^2/(6"D")`

• `"d"^2/(15"D")`

Answer 1

In Young's double slit experiment fifth dark fringe is formed opposite to one of the slits. If D is the distance between the slits and the screen and d is the separation between the slits, then the wavelength of light used is `underline("d"^2/(9"D"))`.

Explanation:

Position of nth dark fringes in Young's double slit experiment is given,

`x_"n" = "D"/"d" (2"n" - 1)lambda/2`

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

Since, fifth dark fringe is formed opposite to one of the slit,

∴ 2x⁵ = d [distance between slits]

Put n = 5 in Eq. (i), we get

`lambda = (2 x_5 "d")/("D"(2 xx 5 - 1))`

`= ("d" * "d")/("D"(10 - 1))`   ...[since, 2x₅ = d]

`= "d"^2/("9D")`