In Young's double slit experiment light of wavelength 500 ~nm is used to form interference pattern. A uniform glass plate of refractive index 1.5 and thickness 0.1 ~mm is introduced in the path of one of the interfering beams. The number of fringes that will shift due to this is

Step-by-step solution

The shift in the interference pattern in Young's double slit experiment when a glass plate of thickness t and refractive index is introduced in the path of one of the beams is given by the formula: x = ( - 1)tD d The number of fringes shifted N is given by the ratio of the shift x to the fringe width = D d . N = x = ( - 1)tD/d D/d = ( - 1)t Given values are = 1.5 , t = 0.1 mm = 0.1 10⁻³ m = 10⁻⁴ m , and = 500 nm = 500 10⁻⁹ m = 5 10⁻⁷ m . Substituting these values into the formula: N = (1.5 - 1) 10⁻⁴ 5 10⁻⁷ N = 0.5