An object is placed at a distance of $20 \ cm$ from a convex lens of focal length $10 \ cm$. The image is formed on the other side of the lens at a distance of . . . . . . $cm$.

Derive the thin lens equation.

Parallel rays are incident on a thick plano-convex lens having radius of curvature $R$,refractive index $\mu$ and thickness $t$. When rays are incident on the plane surface,they converge at a distance $x$ from the plane surface. When rays are incident on the curved surface,they converge at a distance $y$ from the curved surface. Then:

$A$ convex lens of focal length $0.15 \,m$ is made of a material of refractive index $\frac{3}{2}$. When it is placed in a liquid, its focal length is increased by $0.225 \,m$. The refractive index of the liquid is

An object approaches a convergent lens from the left of the lens with a uniform speed $5 \ m/s$ and stops at the focus. The image:

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