Education and Career Forum

The distance between two consecutive bright bands in a biprism experiment is 0.32mm when red light of wavelength 6400amstrong is used. By how much will this distance change if the light is substituted by blue light of wavelength 4800amstrong with same setting.

In the biprism experiment, fringes are the alternate bright & dark bands caused by the light. The fringe width is the distance between two consecutive fringes. In the biprism experiment, the fringe width is given by,
X = Dλ/d
where, Distance between slits = d Distance between slit and screen = D Wavelength of light = λ
Fringe width = X
Here, for same apparatus setting
Let - X1 = Dλ1/d ………….. (1)
X2 = Dλ2/d ………….. (2)
Dividing equation (2) by (1)
We get,
X2 / X1 = (Dλ2/d) x (d/Dλ1)
X2 / X1 = λ2/λ1
∴ X2 = (λ2/λ1) × X1
= (4800/6400) × 0.32
∴ X2 = 0.24mm
∴ Change in fringe width = ∆X
= X1 – X2
= 0.32 - 0.24
∴ ∆X = 0.08mm
The distance between two consecutive bright bands will change by 0.08mm