$A$ point object is held above a thin equiconvex lens at its focus. The focal length is $0.1 \ m$ and the lens rests on a horizontal thin plane mirror. The final image will be formed at

An object is placed at a distance of $12 \,{cm}$ from a convex lens. $A$ convex mirror of focal length $15 \,{cm}$ is placed on the other side of the lens at $8 \,{cm}$ as shown in the figure. The image of the object coincides with the object. When the convex mirror is removed,a real and inverted image is formed at a position. The distance of this image from the object will be ..... $(cm)$.

The final image of the object forms on the object itself. If the focal length of the lens is $30 \ cm$,then the radius of curvature of the mirror is .... $cm$.

$A$ thin convex lens of focal length $f$ is placed on a plane mirror as shown in the figure. When an object is kept at a distance $a$ from the lens-mirror combination,its image is formed at a distance $a/3$ in front of the combination. The value of $a$ is

$A$ concave mirror of focal length $f_{1}$ is placed at a distance $d$ from a convex lens of focal length $f_{2}$. $A$ parallel beam of light coming from infinity parallel to the principal axis falls on the convex lens and then after refraction falls on the concave mirror. If the light is to retrace its path,the distance $d$ should be:

Consider a concave mirror and a convex lens (refractive index $=1.5$) of focal length $10 \ cm$ each,separated by a distance of $50 \ cm$ in air (refractive index $=1$) as shown in the figure. An object is placed at a distance of $15 \ cm$ from the mirror. Its erect image formed by this combination has magnification $M_1$. When the setup is kept in a medium of refractive index $7/6$,the magnification becomes $M_2$. The magnitude $\left|\frac{M_2}{M_1}\right|$ is