Question

Green light of wavelength 5100 Å from a narrow slit is incident on a double slit. If the overall separation of 10 fringes on a screen 2 m away is 2 cm. Find the slit separation.

Answer 1

To find the slit separation (d) in a double-slit experiment, we use the fringe width formula: 

`beta = (lamdaD)/d`

Given:

Wavelength of green light: λ = 5100 Å = 5100 × 10⁻¹⁰ m

Distance between the slits and the screen: D = 2

Separation of 10 fringes: 2 cm = 0.02 m

Fringe width:

`beta = ("Total Fringe Separation")/("Number of Fringers") = 0.02/10 = 0.002` m

`d = (lambdaD)/beta`

Substituting values: 

`d = ((5100 xx 10^(-10))xx2)/(0.002)`

`d = (10200 xx 10^-10)/(0.002)`

`d = (10200 xx 10^(-10))/(2 xx 10^(-3))`

`d = (10200)/2 xx 10^(-7)` m

`d = 5.1 xx 10^(-4)` m = 0.51 mm