A convex lens forms a real image $16\mathrm{mm}$ long on a screen. If the lens is shifted to a new position without disturbing the object or the screen then again a real image of length $81\mathrm{mm}$ is formed. The length of the object must be

A point object is moving with speed $u_0$ at a position somewhere between $2F$ and $F$ in front of a convex lens. The speed of its image is

If ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ are the radii of curvature of the spherical surfaces of a thin lens and ${\mathrm{R}}_1>{\mathrm{R}}_2$, then this lens can