Which of the following statements about light waves is $NOT$ correct?

The radius of curvature of a spherical mirror is half of the focal length.

Draw ray diagrams showing the image formation by a concave mirror when an object is placed:
$(a)$ Between pole $(P)$ and focus $(F)$ of the mirror.
$(b)$ Between focus $(F)$ and centre of curvature $(C)$ of the mirror.
$(c)$ At centre of curvature $(C)$ of the mirror.
$(d)$ $A$ little beyond centre of curvature $(C)$ of the mirror.
$(e)$ At infinity.

$(a)$ $A$ concave mirror produces a three times enlarged real image of an object placed at $10\, cm$ in front of it. Calculate the focal length of the mirror.
$(b)$ Show the formation of the image with the help of a ray diagram when an object is placed $6\, cm$ away from the pole of a convex mirror.

$A$ $10 \, cm$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $30 \, cm$. The distance of the object from the lens is $20 \, cm$. Find the $(i)$ position,$(ii)$ nature,and $(iii)$ size of the image formed.

If the radius of curvature of a concave mirror is $36\, cm$,what is its focal length (in $, cm$)?