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.

$A$ narrow parallel beam of light is incident paraxially on a solid transparent sphere of radius $r$ kept in air. What should be the refractive index if the beam is to be focused at the farther surface of the sphere?

$A$ 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:

$A$ curved surface of radius $R$ separates two media of refractive indices $\mu_1$ and $\mu_2$ as shown in figures $A$ and $B$. Choose the correct statement$(s)$ related to the real image formed by the object $O$ placed at a distance $x$,as shown in figure $A$.

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 $cm$)

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.