An 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 formed by the combination coincides with the object itself. The focal length of the convex mirror is.....$cm$

When light is incident on a medium at angle $i$ and refracted into a second medium at an angle $r$,the graph of $\sin i$ vs $\sin r$ is as shown in the figure. From this,one can conclude that:

The object distance $u$,the image distance $v$,and the magnification $m$ in a lens follow certain linear relations. These are:

Which of the following is correct regarding microscope and telescope?

$A$ plane mirror is placed $22.5\; cm$ in front of a concave mirror of focal length $10\; cm$. An object is placed between the two mirrors such that the images formed by both mirrors coincide. Find the magnification of the image produced by the concave mirror.

The $45^{\circ}-45^{\circ}-90^{\circ}$ prism of height $10 \,cm$ (see image) has a refractive index $\mu = 2$,with a silvered hypotenuse surface. $A$ convex lens of focal length $10 \,cm$ is placed $15 \,cm$ in front of a wall. The system produces a sharp image of point $P$ on the wall. The value of $h$ (in $cm$) is closest to: