Question

White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringes. The difference in wavelengths of red and violet light is ______ nm.

Options

• 100

• 200

• 300

• 400

Answer 1

White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringes. The difference in wavelengths of red and violet light is 300 nm.

Explanation:

Position of first bright mrge = `(lambdaD)/d`

So position of first red frirge = `Y_R = (lambda_RD)/d` ....(i)

Position of first violet fringe = `Y_"v" = (lambda_"v"D)/d`...(ii)

by using eqn (i) and eqn (ii),

`Y_R - Y"v" = (lambda_R - lambda_"v")D/d`

`(Y_R - Y_"v")d/D = lambda_R - lambda_"v"`

`lambda_R - lambda_"v" = ((3.5 - 2))/1.5 xx 0.3 xx 10^-3` mm

`lambda_R - lambda_"v" = 0.3 xx 10^-3` mm

`Deltalambda = lambda_R - lambda_"v"` = 300 nm