A two-slit Young's interference experiment is done with monochromatic light of wavelength $6000 \stackrel{\circ }{\mathrm{A}}$. These slits are $2 \mathrm{mm}$ apart. The fringes are observed on a screen placed $10 \mathrm{cm}$ away from the slits. A transparent plate of thickness of $0.5 \mathrm{mm}$ is placed in front of one of the slits. It is found that the interference pattern shifts by $5 \mathrm{mm}$. What is the refractive index of the transparent plate?