How to Calculate the Distance of the Screen in a Double-Slit Experiment?

What is the distance between the double slit and the screen if the 4th fringe is measured to be 42.2 cm from the center fringe?

The distance between the double slit and the screen is approximately 0.557 meters.

Explanation:

To determine the distance to the screen, we can use the formula for the fringe spacing in a double-slit interference pattern:

x = (m * λ * L) / d

Where:

x is the distance from the center fringe to the m-th fringe (in this case, the 4th fringe).

λ is the wavelength of the laser light (633 nm or 633 × 10^(-9) m).

L is the distance between the double slit and the screen (which we want to find).

d is the slit separation (42 μm or 42 × 10^(-6) m).

Rearranging the equation to solve for L:

L = (x * d) / (m * λ)

Substituting the given values:

L = (42.2 cm * 42 × 10^(-6) m) / (4 * 633 × 10^(-9) m)

Calculating the result:

L ≈ 0.557 m

Therefore, the distance between the double slit and the screen is approximately 0.557 meters.