Combinations of Mirrors and Thin Lenses

Which of the following can form diminished, virtual and erect image of your face

A flat mirror $M$ is arranged parallel to the wall $W$ at a distance $l$ from it. The light produced by a point source $\mathrm{S}$ kept on the wall is reflected by the mirror and produces a light spot on the wall. The mirror moves with velocity $v$ towards the wall.

It is desired to make an achromatic combination of two lenses $(L_1 \& L_2)$ ${\omega }_1$ and ${\omega }_2 (<{\omega }_1)$. If the combination of lenses is converging then

A planoconvex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length $28 \mathrm{cm}$. When its curved surface is silvered and the plane surface not silvered, it is equivalent to a concave mirror of focal length $10 \mathrm{cm}$, then the refractive index of the material of the lens is

An object is placed in front of a thin convex lens of focal length 30 cm and a plane mirror is placed 15 cm behind the lens. If the final image of the object coincides with the object, the distance of the object from the lens is

A object is placed at a distance of 15 cm from a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at its focus such that the image by the combination coincides with the object itself. The focal length of the convex mirror is

A double convex lens has focal length of $25.0 \mathrm{cm}$ in air. The radius of one of the surfaces is double of the other. Find the radii of curvature, if the refractive index of the material of the lens is $1.5$.

Which of the following expression is correct for :

Taking the rays as incident from a medium of refractive index  $n_1$  to another of refractive index  $n_2$

An illuminated object and a screen are placed $90 \mathrm{cm}$ apart. The focal length and nature of the lens required to produce a clear image on the screen, twice the size of the object would be:

A given ray of light suffers minimum deviation in an equilateral prism $P$. Additional prism $Q$ and $R$ of identical shape and of the same material as $P$ are now added as shown in the figure. The ray will now suffer

An eye specialist prescribes spectacles having a combination of convex lens of focal length 40 cm in contact with a concave lens of focal length 25 cm. The power of this lens combination in diopters is

A thin plane convex glass lens $\left(\mu =1.5\right)$ has its plane surface silvered and $R$ is the radius of curvature of the curved part. Then which of the following ray diagram is the correct representation for an object placed at $O$.

A biconvex lens of radius of curvature $R$is made up of a variable refractive index $\mu =2\left(1+\frac{\left|y\right|}{d}\right)$. Assume $2 d<<R$. A point object is placed at $R=1 \mathrm{m}$ on the principal axis as shown in figure. If the spread of image lies over a span of $n$ meter along the axis, then find the value of $n$.

The radius of curvature of convex surface of a Plano-convex lens is $15 \mathrm{cm}$. The $\mathrm{R}.\mathrm{I}.$ of material of lens is $\frac{3}{2}$. When kept in air has focal length $f$. If plane surface is silvered and lens is kept in a large medium of $\mathrm{R}.\mathrm{I}.$ $=2$, it behave as a mirror of power $P$

A tube of length $30 \mathrm{cm}$ has its inner lateral surface blackened. Two lenses of focal lengths $10 \mathrm{cm}$ and $20 \mathrm{cm}$ are fixed at the ends of the tube. For same beam, intensities of spots on screen are $I_1$ and $I_2$ for arrangement $\left(1\right)$ and arrangement $\left(2\right)$. If the ratio of $I_2 : I_1$ is of the form $N^2\text{,}$ find $N$.

A real image of an object is formed at a distance of $20 \mathrm{c}\mathrm{m}$ from a lens. On putting another lens in contact with it, image is shifted $10 \mathrm{c}\mathrm{m}$ towards the combination. The power of the lens is _____ $\mathrm{D}$.

Consider a concave mirror and a convex lens (refractive index = $1.5$) of focal length $10$ $\mathrm{cm}$ each, separated by a distance of $50$ $\mathrm{cm}$ in air (refractive index = $1$), as shown in the figure. An object is placed at a distance of $15$ $\mathrm{cm}$ from the mirror. Its erect image, formed by this combination, has magnification ${\mathrm{M}}_1$ . When the set-up is kept in a medium of refractive index $\frac{7}{6}$ , the magnification becomes ${\mathrm{M}}_2$. The magnitude $\left|\frac{{\mathrm{M}}_2}{{\mathrm{M}}_1}\right|$ is

A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. The refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both the curved surfaces are of the same radius of curvature, $R=14 \mathrm{cm}$. For this bi-convex lens, for an object distance of $40 \mathrm{cm}$, the image distance will be,

A combination of two thin convex lenses of focal length $0.3$ $m$ and $0.1 m$ will have minimum spherical and chromatic aberrations if
the distance between them is