$A$ 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:

$A$ point object is kept at $P$ in front of a glass sphere of radius $R$. Its image is formed at $Q$ such that $PO = QO$. The refractive index of the material of the glass sphere is $1.4$. The distance $PO$ is equal to:

$A$ spherical convex surface of power $5 \text{ dioptre}$ separates object and image space of refractive indices $1.0$ and $\frac{4}{3}$ respectively. The radius of curvature of the surface is (in $\text{ cm}$)

$A$ small object is embedded in a glass sphere $(\mu = 1.5)$ of radius $5.0\, cm$ at a distance $1.5\, cm$ to the left of the centre. Locate the image of the object as seen by an observer standing to the left of the sphere.

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

$A$ 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 $B$.