Explanation of Young's Double Slit Experiment:

In Young's double slit experiment, a coherent light source, such as a laser, is directed towards a barrier with two narrow slits. The light passing through the slits creates an interference pattern on a screen placed behind the barrier. This pattern consists of alternating bright and dark fringes.

Fringe Width:

The fringe width (W) is the distance between two consecutive bright fringes or two consecutive dark fringes in the interference pattern. It can be calculated using the formula:

W = λ * D / d

Where:
- λ is the wavelength of light
- D is the distance between the screen and the double slits
- d is the distance between the two slits

Given that the fringe width is 2 mm, we can rearrange the formula to solve for d:

d = λ * D / W

Finding the Distance of the Second Dark Fringe:

To find the distance of the second dark fringe from the central fringe, we need to determine the order of the fringe (n) and then calculate the corresponding position.

The order of the fringe can be determined by the formula:

n = (x - x₀) / W

Where:
- x is the distance of the fringe from the central fringe
- x₀ is the distance of the central fringe from the center of the screen

For the second dark fringe (n = -2), we can rearrange the formula to solve for x:

x = n * W + x₀

Calculation:

Let's say the central fringe is at distance x₀ = 0 mm.

For the second dark fringe (n = -2):
x = -2 * 2 mm + 0 mm = -4 mm

Since distance cannot be negative, we take the magnitude:
|x| = 4 mm

Therefore, the distance of the second dark fringe from the central fringe is 4 mm.

Conclusion:

In Young's double slit experiment, the distance of the second dark fringe from the central fringe is 4 mm. This can be calculated using the formula for fringe width and the order of the fringe. The second dark fringe is located on the opposite side of the central fringe and forms part of the interference pattern created by the light passing through the double slits.