For a prism, a graph between angle of deviation $\left(\delta \right)$ and angle of incidence will be

A point object $O$ is placed in front of a glass rod having a spherical end of the radius of curvature $30 \mathrm{cm}$. The image would be formed 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:

A biconvex lens is cut into two halves along $\left(\mathrm{i}\right) XOX\text{'}$ and $\left(\mathrm{ii}\right) YOY\text{'}$ as shown in the figure. Let $f$, $f\text{'}$, $f\text{'}\text{'}$ be the focal lengths of the complete lens, of each half in case $\left(\mathrm{i}\right)$, and of each half in case $\left(\mathrm{ii}\right)$, respectively. Choose the correct statement from the following:-