$A$ point object is moving at a constant speed of $1 \,ms^{-1}$ along the principal axis of a convex lens of focal length $10 \,cm$. The speed of the image is also $1 \,ms^{-1}$, when the object is at what distance (in $cm$) from the optical centre of the lens?

An object is placed at a distance of $4\,cm$ in front of a concave lens of focal length $12\,cm$. The nature and position of the image from the lens is

$A$ thin convex lens is made of a material of refractive index $1.6$. An object is kept at a distance of $u$ from the lens on the principal axis as shown in the figure. The radii of curvature of the surfaces are $10 \, cm$ and $5 \, cm$. Now,the lens is reversed such that the face having radius of curvature $5 \, cm$ lies close to the object. The difference in image position as obtained for both the cases is equal to ......$u$.

An object is placed first at infinity and then at $20 \ cm$ from the object-side focal plane of a convex lens. The two images thus formed are $5 \ cm$ apart. The focal length of the lens is $...... \ cm$.

In an experiment to measure the focal length $(f)$ of a convex lens,the magnitude of object distance $(x)$ and the image distance $(y)$ are measured with reference to the focal point of the lens. The $y-x$ plot is shown in the figure. The focal length of the lens is . . . . . . $cm$.

$A$ convex lens forming a real image of magnification $m_1$ on a screen is moved through a distance $x$. $A$ new image of magnification $m_2$ is again formed on the screen. The focal length of the lens is: