Question

In Young's double slit experiment the slits are 0.589 mm apart and the interference is observed on a screen placed at a distance of 100 cm from the slits. It is found that the 9th bright fringe is at a distance of 7.5 mm from the dark fringe which is second from the center of the fringe pattern. Find the wavelength of the light used.

Answer 1

In Young's double slit experiment, the distance of the mth bright fringe from the central fringe is given by:

x = `m("D"lambda)/"d"`    (m = 0, 1, 2, 3,...)

Here, m = 9

`therefore x = 9 ("D"lambda)/"d"`

The distance of mth dark fringe from the central fringe

x' = `("m" - 1/2)("D"lambda)/"d"`    (m = 1, 2, 3,...)

Here, m = 2

x' = `(2 - 1/2) ("D"lambda)/"d" = 3/2 ("D"lambda)/"d"`

According to question, we have:

`9 ("D"lambda)/"d" - 3/2 ("D"lambda)/"d" = 7.5 xx 10^-3`m

or   `15/2 ("D"lambda)/"d" = 7.5 xx 10^-3`m

`lambda = 2/15 xx (7.5 xx 10^-3) xx "d"/"D"`

`= 2/15 xx (7.5 xx 10^-3) xx ((0.589 xx 10^-3))/1`

`= 0.589 xx 10^-6` m

`= 5890 xx 10^-10`m

= 5890 Å