Two objects ${\mathrm{O}}_1$ and ${\mathrm{O}}_2$ are placed in front of a lens of focal length $f.$ The objects are placed on the principal axis such that ${\mathrm{O}}_1{\mathrm{O}}_2=x$ and ${\mathrm{O}}_2$ is closer to the lens. The distance of ${\mathrm{O}}_2$ from lens is greater than its focal length. If their images formed are $I_1$ and $I_2$ such that the distance between them is $I_1{I}_2=y,$ then

. A point object is placed $30 \mathrm{cm}$ in front of an equiconvex lens of radius of curvature $15 \mathrm{cm}$ and made of glass of refractive index $\frac{3}{2}.$ On placing a convex mirror of radius of curvature $15 \mathrm{cm}$ behind the lens on image side as shown in figure, the final image is found to coincide with the object. The possible distance $\mathrm{x}$ between convex lens and convex mirror is

A converging lens is used to form an image on a screen. When the upper half of the lens is covered by an opaque screen

A point object $O$ is placed at a distance of $30 \mathrm{cm}$ from a convex lens of focal length $20 \mathrm{cm},$ cut into two halves each of which is displaced by $5\times {10}^{-2} \mathrm{cm}$ as shown. Choose the correct option(s).

A convex lens $(f=0.15 \mathrm{m})$ and a concave mirror (focal length $=0.3 \mathrm{m}$) are placed so that their optical axes $PQ$ and $RS$ are parallel to each other and separated by $0.6 \mathrm{cm}$ as shown. An lateral object $AB$ of height $1.2 \mathrm{cm}$ is placed on the optical axis $PQ$ at a distance of $0.2 \mathrm{m}$ from lens. If $A\text{'}B\text{'}$ is the image after refraction and reflection then choose the correct option(s).