Question

In Young's double-slit experiment, the distance between the slits is 3 mm and the slits are 2 m away from the screen. Two interference patterns can be obtained on the screen due to light of wavelength 480 nm and 600 run respectively. The separation on the screen between the 5^th order bright fringes on the two interference patterns is ______

Options

• 4 × 10^-4 m 

• 6 × 10⁴ m 

• 12 × 10^-4 m 

• 8 × 10^-4 m 

Answer 1

In Young's double-slit experiment, the distance between the slits is 3 mm and the slits are 2 m away from the screen. Two interference patterns can be obtained on the screen due to light of wavelength 480 nm and 600 run respectively. The separation on the screen between the 5^th order bright fringes on the two interference patterns is 4 × 10^-4 m.

Explanation:

d = 3 mm = 3 × 10^-3 m

D = 1 m λ₁ = 480 nm λ₂ = 600 nm

`""^1lambda_5 = 5 (lambda_1D)/d`

`""^2lambda_5 = 5 (lambda_2D)/d`

`""^2lambda_5 - ""^1lambda_5 = (5D)/d`(600 - 480) nm

= `(5 xx 2)/(3 xx 10^-3) xx 120`

= `10 xx 10^{-3 + 1} xx 4 = 4 xx 10^{5 - 9}`

= `4 xx 10^-4 = 0.4` mm