The same size images are formed by a convex lens when the object is placed at $20\, cm$ or at $10\, cm$ from the lens. The focal length of the convex lens is ............ $cm$.

The radius of curvature for a convex lens is $40 \ cm$ for each surface. Its refractive index is $1.5$. The focal length will be ...... $cm$.

The figure given below shows a beam of light converging at point $P.$ When a concave lens of focal length $16 \ cm$ is introduced in the path of the beam at a place $O$ shown by the dotted line such that $OP$ becomes the axis of the lens,the beam converges at a distance $x$ from the lens. The value of $x$ will be equal to.....$cm$.

For a convex lens,the distance of the object is taken on the $X$-axis and the distance of the image is taken on the $Y$-axis. The nature of the graph so obtained is:

When light rays from the sun fall on a convex lens along a direction parallel to its axis,which of the following statements is true?

In an optical bench experiment, the index error is $+1 \, cm$ and $-1 \, cm$ between the object needle and lens, and between the lens and image needle, respectively. The observed values of $u$ and $v$ are $9 \, cm$ and $17 \, cm$. The focal length of the lens is ..... $cm$.