An object is placed in front of a convex lens,and an image of height $8 \, cm$ is formed. When the lens is moved to a new position,the image height becomes $2 \, cm$. Find the height of the object in $cm$.

$A$ thin converging lens of focal length $25 \,cm$ forms a sharp image of an object on a screen placed at a distance of $75 \,cm$ from the lens. Later, the screen is moved closer to the lens by a distance of $25 \,cm$. The distance through which the object is to be shifted so that its image on the screen is sharp again is

An extended object is placed at point $O$,$10 \ cm$ in front of a convex lens $L_1$ and a concave lens $L_2$ is placed $10 \ cm$ behind it,as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are $20 \ cm$. The refractive index of both the lenses is $1.5$. The total magnification of this lens system is

$A$ convex lens has power $P$. It is cut into two halves along its principal axis. Further,one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in the figure). Choose the incorrect option for the reported pieces.

$A$ diminished image of an object is to be obtained on a large screen $1\, m$ from it. This can be achieved by

$A$ convex lens is made of $3$ layers of glass of $3$ different materials as shown in the figure. $A$ point object is placed on its axis. The number of images of the object formed is: