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

An equiconvex lens of radius of curvature 14 cm is made up of two different materials. Left half and right half of vertical portion is made up of material of refractive index 1.5 and 1.2 respectively as shown in the figure. If a point object is placed at a distance of 40 cm , calculate the image distance.

For a point object, which of the following always produces virtual image in air?

For a given pair of transparent media, the critical angle for which colour is maximum?