If the focal lengths of a lens for red and violet light rays are $f_{R}$ and $f_{V}$ respectively,then which of the following is the true relationship?

$A$ boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length $10\, cm$. The diameter of the sun is $1.39 \times 10^9\, m$ and its mean distance from the earth is $1.5 \times 10^{11}\, m$. What is the diameter of the sun's image on the paper?

$A$ convex lens of focal length $25 \ cm$ and made of glass with refractive index $1.5$ is immersed in water. The absolute change in focal length of the glass is [Use refractive index of water = $\frac{4}{3}$] (in $cm$)

$A$ diminished image of an object is to be obtained on a screen $1.0 \ m$ from it. This can be achieved by appropriately placing

The focal length of a thin biconvex lens is $20 \,cm$. When an object is moved from a distance of $25 \,cm$ in front of it to $50 \,cm$, the magnification of its image changes from $m_{25}$ to $m_{50}$. The ratio $\frac{m_{25}}{m_{50}}$ is

An object placed $10 \ cm$ in front of a lens has an image $20 \ cm$ behind the lens. What is the power of the lens (in dioptres)?