A plano-convex lens (focal length $f_2$. refractive index $n_2$, radius of curvature $R$) fits exactly into a plano-concave lens (focal length $f_1$’ refractive index $n_1$, radius of curvature $R$). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

An object is at a distance of $20 \mathrm{m}$ from a convex lens of focal length $0.3 \mathrm{m}$. The lens forms an image of the object. If the object moves away from the lens at a speed of $5 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$, the speed and direction of the image will be:

Two similar thin equi-convex lenses, of focal length $f$ each, are kept coaxially in contact with each other such that the focal length of the combination is $f_1$. When the space between the two lenses is filled with glycerine (which has the same refractive index ($n=1.5$) as that of glass) then the equivalent focal length is $f_2$. The ratio $f_1:f_2$ will be:

One plano-convex and one plano-concave lens of same radius of curvature ‘$R$’ but of different materials are joined side-by-side as shown in the figure.If the refractive index of the material of $1$ is $n_1$ and that of $2$ is $n_2$, then the focal length of the combination is:

The graph shows how the magnification $m$ produced by a thin lens varies with image distance $u$. What is the focal length of the lens used?

A thin convex lens $L$ (refractive index $=1.5$) is placed on a plane mirror $M$. When a pin is placed at $A$, such that $OA=18 \mathrm{cm}$, its real inverted image is formed $M$ at $A$ itself, as shown in figure. When a liquid of refractive index $n_1$ is put between the lens and the mirror. The pin has to be moved to $A’$, such that $OA’=27 \mathrm{cm}$, to get its inverted real image at $A’$ itself. The value of $n_1$ will be:

A convex lens (of focal length $20 \mathrm{cm}$) and a concave mirror, having their principal axes along the same lines, are kept $80 \mathrm{cm}$ apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of $30 \mathrm{cm}$ to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be:

What is the position and nature of image formed by lens combination shown in figure? ($f_1$, $f_2$ are focal lengths)

A plano-convex lens is made of a material of refractive index $n$. When a small object is placed $30 \mathrm{cm}$ away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of $10 \mathrm{cm}$ away from the lens. Which of the following statement(s) is(are) true?