If the image of an object is at the focal point $f$ to the right side of a convex lens, the position of the object on the left of the lens is at

An object is placed at a distance of $10 \, cm$ from a lens. The image is formed at a distance of $20 \, cm$ behind the lens. The power of the lens is ......

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

$f_V$ and $f_R$ are the focal lengths of a convex lens for violet and red light respectively,and $F_V$ and $F_R$ are the focal lengths of a concave lens for violet and red light respectively. Then:

Explain how the image is formed by a thin convex lens and derive the lens maker's formula: $\frac{1}{f} = (n_{21} - 1) \left[ \frac{1}{R_1} - \frac{1}{R_2} \right]$.

The focal lengths of a converging lens are $f_V$ and $f_R$ for violet and red light,respectively. Which of the following relations is correct?