$A$ spherical vessel of radius $10 \, cm$ is filled with water of refractive index $\mu = 4/3$. $A$ fish is at a distance of $4 \, cm$ from the center as shown in the figure. If viewed from end $E$,at what distance will the fish appear to be (in $, cm$)? (Neglect the thickness of the vessel)

$A$ 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 . . . . . . .

Light from a point source in air falls on a spherical glass surface ($n = 1.5$ and radius of curvature $= 20\; cm$). The distance of the light source from the glass surface is $100\; cm$. At what position (in $cm$) the image is formed?

Find the image distance in $cm$ for the given refraction through a spherical surface.

$A$ clear transparent glass sphere $(\mu=1.5)$ of radius $R$ is immersed in a liquid of refractive index $1.25$. $A$ parallel beam of light incident on it will converge to a point. The distance of this point from the center will be

$A$ spherical surface of radius of curvature $R$ separates air (refractive index $1.0$) from glass (refractive index $1.5$). The centre of curvature is in the glass. $A$ point object $P$ placed in air is found to have a real image $Q$ in the glass. The line $PQ$ cuts the surface at a point $O$,and $PO = OQ$. The distance $PO$ is equal to (in $R$)