Question:

A beam of light with wavelength λ = 600 nm is incident on a double slit setup, as shown below. The distance between the two slits is d = 0.2 mm. The screen is placed L = 1 m away from the double slits.

a) Calculate the angular separation (θ) between the first and second-order bright fringes observed on the screen.

b) Determine the distance (y) from the central bright fringe to the fourth-order bright fringe on the screen.

Assume the interference pattern is formed on a large screen.

Answer:

a) To calculate the angular separation between the first and second-order bright fringes observed on the screen, we can use the equation:

θ = λ / d

Given that the wavelength λ = 600 nm (or 600 x 10^-9 m) and the distance between the two slits d = 0.2 mm (or 0.2 x 10^-3 m), we substitute these values into the equation:

θ = (600 x 10^-9 m) / (0.2 x 10^-3 m)

θ = 0.003 radians

Thus, the angular separation between the first and second-order bright fringes is 0.003 radians.

b) To determine the distance from the central bright fringe to the fourth-order bright fringe on the screen, we can use the equation:

y = (mλL) / d

where m is the order of the bright fringe.

Given that m = 4, λ = 600 nm (or 600 x 10^-9 m), L = 1 m, and d = 0.2 mm (or 0.2 x 10^-3 m), we substitute these values into the equation:

y = (4 x 600 x 10^-9 m x 1 m) / (0.2 x 10^-3 m)

y = 0.012 m

Thus, the distance from the central bright fringe to the fourth-order bright fringe on the screen is 0.012 m.