A certain pair of slits are separated by a distance d. Monochromatic coherent light falls on this pair of slits and the interference pattern is observed on a screen. The separation distance between adjacent bright fringes near the center of that interference pattern on the screen is found to be 2.0 mm. Then the slits are replaced by another pair of slits; these slits are separated by a distance one-half that of the original pair. The interference pattern is again observed. What is the new separation distance between adjacent bright fringes

The new separation distance between adjacent bright fringes will be 4 mm

Explanation:

Since, the distance between adjacent bright fringes is given by the formula:

Δx₁ = λL/d = 2 mm   eqn (1)

where,

Δx = Distance between adjacent bright fringes

λ = wavelength of light = constant for both cases

L = Distance between the slits and the screen

d = slit separation

Now, for the second case:

Slit Separation = d/2

Therefore,

Δx₂ = λL/(d/2)

Δx₂ = 2(λL/d)

using eqn (1), we get:

Δx₂ = 2 Δx₁

Δx₂ = 2(2 mm)

Δx₂ = 4 mm

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