A thin prism $P_1$ with angle $4°$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of prism $P_2$ is

The angle of a prism is ‘$A$’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index $n$, of the prism is:

A ray falls on a prism $\mathrm{ABC}$ $(\mathrm{AB} = \mathrm{BC})$ and travels as shown figure. The minimum refractive index of the prism material should be

A point object $O$ is placed in front of a glass rod having a spherical end of the radius of curvature $30 \mathrm{cm}$. The image would be formed be