Light of wavelength 575 nm falls on two double slits spaced 0.30 mm apart. What is the required distance from the slits to a screen if the spacing between the first and second dark fringe is to be 4.00 mm

L = 2.1 m

Explanation:

From Young's Double Slit Experiment, the formula for the distance between two consecutive dark or bright fringes, called fringe spacing, is derived as:

Δx = λL/d

where,

Δx = distance between first and second dark fringe = 4 mm = 4 x 10⁻³ m

λ = wavelength of light = 575 nm = 5.75 x 10⁻⁷ m

d = distance between the slits = 0.3 mm = 3 x 10⁻⁴ m

L = Distance from slits to screen = ?

Therefore,

4 x 10⁻³ m = (5.75 x 10⁻⁷ m)(L)/(3 x 10⁻⁴ m)

L = (4 x 10⁻³ m)/(1.92 x 10⁻³)

L = 2.1 m