Light of wavelength 560 nm passes through a pinhole of diameter 0.20 mm and strikes a wall located at a distance of 2.00 m . Determine the diameter of the central bright spot formed on the wall.

Step-by-step solution

The angular radius of the central bright spot (Airy disk) formed by diffraction through a circular aperture (pinhole) is given by: = 1.22 d where is the wavelength of light and d is the diameter of the pinhole. The linear radius of the central bright spot on a screen at a distance D is: R = D = 1.22 D d The diameter of the central bright spot is: D_ spot = 2R = 2.44 D d Given values: = 560 nm = 560 10⁻⁹ m d = 0.20 mm = 0.20 10⁻³ m D = 2.00 m Substituting the values into the formula: D_ spot = 2.44 560 10⁻⁹ 2.00 0.2