In determining the refractive index of a glass slab using a travelling microscope, the following readings are tabulated

(a) Reading of travelling microscope for ink mark $=5.123 \mathrm{~cm}$

(b) Reading of travelling microscope for ink mark through glass slab $=6.123 \mathrm{~cm}$

(c) Reading of travelling microscope for chalk dust on glass slab $=8.123 \mathrm{~cm}$

From the data, the refractive index of a glass slab is

The final image formed by an astronomical telescope is

If the angle of minimum deviation is equal to angle of a prism for an equilateral prism, then the speed of light inside the prism is

A luminous point object $O$ is placed at a distance $2 R$ from the spherical boundary separating two transparent media of refractive indices $n_1$ and $n_2$ as shown, where $R$ is the radius of curvature of the spherical surface. If $n_1=\frac{4}{3}, n_2=\frac{3}{2}$ and $R=10 \mathrm{~cm}$, the image is obtained at a distance from $P$ equal to