A screen is placed 50cm from a single slit illuminated with 690nm light. If the distance between the first and third dark fringes in the diffraction pattern is 3mm.

a) Find the width of the slit

used w = (2/lambdaL) / d to get 500 mm

b) Find the width of the central bright fringe using w = (2/lambdaL) / d.

a) Distance of screen (D) = 50 X 10⁻²

Wavelength of light λ = 690 x 10⁻⁹

d = width of slit

Distance between first and third dark fringe = 2 x fringe width

= 2 x λD/d = 3 x 10⁻³

d = 2 x 690 x 10⁻⁹ x 50 x 10⁻² / 3 x 10⁻³ = 0.23 mm

b) Width of central bright fringe = 2 λD/d

2 x 690 x 10⁻⁹ x 50 x 10⁻² / 23 x 10⁻⁵ m

= 3 mm.