In the displacement method,a convex lens forms a real image of an object for its two different positions. If the heights of the images in the two cases are $24 \,cm$ and $6 \,cm$,then the height of the object is ........ $cm$.

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 and a screen are fixed on the uprights of an optical bench. The distance between them is $100 \, cm$. $A$ convex lens is placed in between the object and the screen and the position of the lens is so adjusted that the image of the object is formed on the screen at two conjugate positions of the lens. The distance between these conjugate positions of the lens is $40 \, cm$. What is the focal length of the lens in $cm$?

$A$ convex lens is used to form a real image of an object on a screen. It is observed that even when the positions of the object and the screen are fixed,there are two positions of the lens that form real images. If the heights of the images are $4 \ cm$ and $9 \ cm$ respectively,the height of the object is.....$cm$.

The dotted part of the lens is cut and kept on the $x$-axis as shown in the diagram. If parallel paraxial rays are falling on this system,then the coordinate of the image formed after refraction from both the lenses is $(30, -1)$. If $x = 2.5 \, cm$,then $y = .......... \, cm$. (Assume the lens has no spherical aberration)

$A$ point object $O$ is placed on the principal axis of a convex lens of focal length $20 \, cm$ at a distance of $40 \, cm$ to the left of it. The diameter of the lens is $10 \, cm$. If the eye is placed $60 \, cm$ to the right of the lens at a distance $h$ below the principal axis,then the maximum value of $h$ to see the image will be.......$cm$.