$A$ 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

$A$ point object $O$ is placed in front of a glass rod having a spherical end of radius of curvature $30 \,cm$. The image would be formed at

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 $R$)

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

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

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 $, cm$)?