Question

Light of wavelength 617 nm passes through a slit 6.30 × 10-6 m wide and falls on a screen that is 2.83 m away. What is the distance on the screen from the center of the central bright fringe to the thrid dark fringe on either side?

Answer 1

To find the distance on the screen from the center of the central bright fringe to the third dark fringe on either side, first calculate the angle of diffraction for the central bright fringe using the formula θ = sin^-1(mλ / w). Then, use this angle to find the distance between the central bright fringe and the third dark fringe on either side using the formula y = Dθ. Finally, calculate the total distance on the screen by multiplying y by 3.

Step-by-step explanation:

First, we need to calculate the angle of diffraction for the central bright fringe. We can use the formula: θ = sin-1(mλ / w), where θ is the angle of diffraction, m is the order of the fringe, λ is the wavelength, and w is the width of the slit. Plugging in the values, we get θcentral = sin-1(1 * 617 × 10-9 / 6.30 × 10-6).

Then, we can use this angle to find the distance between the central bright fringe and the third dark fringe on either side. We can use the small angle approximation: y = Dθ, where y is the distance from the center of the bright fringe to the dark fringe, D is the distance from the slit to the screen, and θ is the angle of diffraction. Plugging in the values, we get y = 2.83 * tan(θcentral).

Finally, we can calculate the total distance on the screen from the center of the central bright fringe to the third dark fringe on either side by multiplying the distance y by 3. Plugging in the value, we get the final result: total distance = 3 * y.