$A$ spherical surface of radius of curvature $R$ separates air (refractive index $n_1 = 1.0$) from glass (refractive index $n_2 = 1.5$). The center of curvature is inside the glass. $A$ point object placed at $P$ forms a real image at $Q$. The line $PQ$ intersects the surface at $O$ and $PO = OQ$. The distance $PO$ is:

$A$ curved surface of radius $R$ separates two media of refractive indices $\mu_1$ and $\mu_2$ as shown in figures $A$ and $B$. Choose the correct statement$(s)$ related to the virtual image formed by object $O$ placed at a distance $x$,as shown in figure $A$.

Two identical glass rods $S_1$ and $S_2$ (refractive index $= 1.5$) have one convex end of radius of curvature $10 \ cm$. They are placed with the curved surfaces at a distance $d$ as shown in the figure,with their axes (shown by the dashed line) aligned. When a point source of light $P$ is placed inside rod $S_1$ on its axis at a distance of $50 \ cm$ from the curved face,the light rays emanating from it are found to be parallel to the axis inside $S_2$. The distance $d$ is (in $cm$)

$A$ spherical surface separates two media of refractive indices $1$ and $1.5$ as shown in the figure. Find the distance of the image of an object $O$ from the spherical surface. ($C$ is the center of curvature of the spherical surface and $R$ is the radius of curvature).

Light from a point source in air falls on a convex curved surface of radius $20 \,cm$ and refractive index $1.5$. If the source is located at $100 \,cm$ from the convex surface,the image will be formed at what distance from the object?

In a thin spherical fish bowl of radius $10 \, cm$ filled with water of refractive index $\mu = \frac{4}{3}$,there is a small fish at a distance of $4 \, cm$ from the center as shown in the figure. Where will the image of the fish appear if seen from point $F$ (in $, cm$)?