Separated by a distance of 1.0 cm , two narrow slits emit light in phase. The light has a wavelength of 5.0 10⁻⁷ m . An interference pattern is formed on a screen positioned 1.0 m away. Determine the separation between consecutive maxima and whether one can expect to distinguish between these maxima with the naked eye.

Step-by-step solution

Given: Distance between slits, d = 1.0 cm = 1.0 10⁻² m Wavelength, = 5.0 10⁻⁷ m Distance to screen, D = 1.0 m The separation between consecutive maxima is the fringe width, given by: = D d Substituting the given values: = 5.0 10⁻⁷ 1.0 1.0 10⁻² = 5.0 10⁻⁵ m = 0.05 10⁻³ m = 0.05 mm The resolution limit of the human eye is approximately 0.1 mm . Since the fringe width 0.05 mm is less than the resolution limit of the human eye, the consecutive maxima cannot be distinguished with the naked eye.