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:

$A$ spherical surface of radius of curvature $10\,cm$ separates two media $X$ and $Y$ of refractive indices $3/2$ and $4/3$ respectively. The centre of the spherical surface lies in the denser medium. An object is placed in medium $X$. For the image to be real,the object distance must be:

$A$ laser beam falls on a crystal ball of radius $R$ as shown in the figure. What is its refractive index?

$A$ parallel beam of light travelling in water (refractive index $\mu_1 = 4/3$) is refracted by a spherical air bubble of radius $R = 2 \, cm$ situated in water. Assuming the light rays to be paraxial,the position of the image due to refraction at the first surface is:

Two identical glass rods $S_1$ and $S_2$ (refractive index $= 1.5$) have one convex end of radius of curvature $10 \ cm$. They are placed with the curved surfaces at a distance $d$ as shown in the figure,with their axes (shown by the dashed line) aligned. When a point source of light $P$ is placed inside rod $S_1$ on its axis at a distance of $50 \ cm$ from the curved face,the light rays emanating from it are found to be parallel to the axis inside $S_2$. The distance $d$ is (in $cm$)

Explain the refraction by two transparent spherically curved surfaces.