$A$ 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 . . . . . . .

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

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 the refractive index $\mu$ of the sphere is varied,then the position $x$ of the object will also vary. Identify the correct statement.

Light from a point source in air falls on a convex spherical glass surface $(\mu = 1.5, R = 20 \, cm)$. The distance of the light source from the glass surface is $100 \, cm$. At what position is the image formed (in $, cm$)?

$A$ spherical surface of radius of curvature $R$ separates air from glass of refractive index $1.5$. The centre of curvature is in the glass. $A$ point object $P$ placed in air forms a real image $Q$ in the glass. The line $PQ$ cuts the surface at point $O$ and $PO = OQ = x$. Hence the distance $x$ is equal to (in $R$)

In a long glass tube,a mixture of two liquids $A$ and $B$ with refractive indices $1.3$ and $1.4$ respectively,forms a convex refractive meniscus towards $A$. If an object placed at $13 \ \text{cm}$ from the vertex of the meniscus in $A$ forms an image with a magnification of $-2$,then the radius of curvature of the meniscus is: