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

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?

$A$ narrow parallel beam of light falls on a glass sphere of radius $R$ and refractive index $\mu$ at normal incidence. The distance of the image from the outer edge is given by

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 $R$)

$A$ point object $O$ is placed on the axis of a cylindrical piece of glass of refractive index $1.6$ as shown in the figure. One surface of the glass piece is convex with a radius of curvature $3 \,mm$. The point appears to be at $5 \,mm$ on the axis when viewed along the axis from the right side of the convex surface. The distance of the point object from the convex surface is: (in $\,mm$)

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