Where is the image formed when an object is placed at a distance of $2f$ in front of a convex mirror?

The figure below shows a point source of light $S$,a convex lens $L$,and a plane mirror $M$. The three are placed such that rays of light from $S$ return to it after reflection from $M$. $(i)$ What is the distance $OS$ called? $(ii)$ To which point (left of $S$,on $S$,or right of $S$) will the rays return if $M$ is moved to the left and brought in contact with $L$?

State Snell's law of refraction.

$A$ $5 \, cm$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $20 \, cm$. The distance of the object from the lens is $30 \, cm$. Find the $(i)$ position,$(ii)$ nature,and $(iii)$ size of the image formed.

Give two uses of a convex lens.

Where is the object placed in a compound microscope?