Optics: JEE Main 2024 Physics question

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 __________ $\mu \mathrm{m}$.