Wave Optics

Monochromatic light of wavelength \(500 \mathrm{~nm}\) is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index \(=1.5\)), the central maximum is shifted to a position previously occupied by the \(4^{\text {th }}\) bright fringe. The thickness of the glass-plate is __________ \(\mu \mathrm{m}\).