$A$ point source of light at the surface of a sphere causes a parallel beam of light to emerge from the opposite surface of the sphere. The refractive index of the material of the sphere is

What is the focal length of this curved surface in $cm$?

$A$ spherical surface of radius of curvature $R$ separates air (refractive index $n_1 = 1.0$) from glass (refractive index $n_2 = 1.5$). The center of curvature is inside the glass. $A$ point object placed at $P$ forms a real image at $Q$. The line $PQ$ intersects the surface at $O$ and $PO = OQ$. The distance $PO$ is:

$A$ parallel beam of light emerges from the opposite surface of the sphere when a point source of light lies at the surface of the sphere. The refractive index of the sphere is

$A$ spherical convex surface of power $5 \text{ dioptre}$ separates object and image space of refractive indices $1.0$ and $\frac{4}{3}$ respectively. The radius of curvature of the surface is (in $\text{ cm}$)

In the figure shown here,a point object $O$ is placed in air. $A$ spherical boundary separates various media with a radius of curvature $2.0 \, m$. $AB$ is the principal axis. The refractive index above $AB$ is $1.6$ and below $AB$ is $2.0$. The separation between the images formed due to refraction at the spherical surface is