$A$ lens of refractive index '$\mu$' has focal length '$f$'. When the lens is immersed in a liquid of refractive index '$\mu_0$',its focal length becomes '$f_0$'. Then '$f_0$' is given by

$A$ point source of light is moving at a rate of $2 \,cm \,s^{-1}$ towards a thin convex lens of focal length $10 \,cm$ along its optical axis. When the source is $15 \,cm$ away from the lens,the image is moving at:

An equiconvex lens is cut into two halves along $(i) XOX'$ and $(ii) YOY'$ as shown in the figure. Let $f, f', f''$ be the focal lengths of the complete lens,of each half in case $(i),$ and of each half in case $(ii),$ respectively. Choose the correct statement from the following:

Letters $A, B, C$ and $D$ are written on a cardboard as shown in the figure. The cardboard is kept at a suitable distance behind a transparent empty glass of cylindrical shape. If the glass is now filled with water,one sees an inverted image of the pattern on the cardboard when looking through the glass. Ignoring magnification effects,the image would appear as:

The objective glass of a telescope is an achromat of focal length $90\,cm$. The magnitudes of dispersive powers of the two lenses are $0.024$ and $0.036$. The focal lengths of the two lenses are:

Define power of a lens and write the $SI$ unit of power.