$A$ spherical interface of radius $R$ separates two media of refractive indices $1$ and $1.4$ respectively, as shown in the figure below. $A$ point source is placed at a distance of $4R$ in front of the spherical interface. The magnitude of the lateral magnification of the point source image is . . . . . . .

An object is placed at $P$ in front of a spherical surface with refractive index $1.5$. Its image is formed at $Q$. If $PO = OQ$,find the distance $PO$. (in $R$)

In the figure shown,$O$ is the centre of the glass sphere. When the spot $P$ on the sphere is viewed almost normally,it appears:

Refer to the figure given below. $\mu_1$ and $\mu_2$ are the refractive indices of air and the lens material, respectively. The height of the image will be . . . . . . cm.

$A$ 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

The figure shows a transparent sphere of radius $R$ and refractive index $\mu$. An object $O$ is placed at a distance $x$ from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface. If an object is placed at a distance $R$ from the pole of the first surface,then the real image is formed at a distance $R$ from the pole of the second surface. The refractive index $\mu$ of the sphere is given by