Two slits separated by a distance of 1mm are illuminated with red light of wavelength 6.5 *10 *(-7) m. The interference fringes are observed on a screen placed 1m from the slits. Find the distance btw the third dark Fringe and the fifth bright fringe on the same side of the central maxima!! :please solve this?

Question

Answer

Key Information:

- Distance between the two slits (d) = 1mm = 0.001m

- Wavelength of the red light (λ) = 6.5 * 10^(-7) m

- Distance between the screen and the slits (L) = 1m

Calculation:

1. Determining Fringe Spacing:
The fringe spacing, also known as the distance between two consecutive fringes, can be calculated using the formula for the double-slit interference pattern:

dsinθ = mλ

Where:
- d is the distance between the slits (0.001m)
- θ is the angle between the central maximum and the mth fringe
- m is the order of the fringe (1, 2, 3, ...)
- λ is the wavelength of light (6.5 * 10^(-7) m)

For the central maximum (m = 0), sinθ = 0, so the first bright fringe occurs when m = 1.

dsinθ = λ

θ = sin^(-1)(λ/d)

Substituting the values, we can find the angle θ:

θ = sin^(-1)(6.5 * 10^(-7) / 0.001)
θ ≈ 0.000409 radians

2. Finding the Distance between Fringes:
The distance between adjacent fringes can be determined using the formula:

y = L * tanθ

Where:
- y is the distance between fringes
- L is the distance between the screen and the slits (1m)
- θ is the angle between the central maximum and the mth fringe (0.000409 radians)

For the third dark fringe (m = 3), the distance from the central maximum can be calculated:

y = 1 * tan(3 * 0.000409)
y ≈ 0.00122m

For the fifth bright fringe (m = 5), the distance from the central maximum can be calculated:

y = 1 * tan(5 * 0.000409)
y ≈ 0.00203m

Final Result:
The distance between the third dark fringe and the fifth bright fringe on the same side of the central maximum is approximately 0.00122m.

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