The primary purpose of using a parabolic mirror in a reflecting telescope is

Assertion : The formula connecting $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason : Laws of reflection are strictly valid for plane surfaces,but not for large spherical surfaces.

Suppose while sitting in a parked car,you notice a jogger approaching towards you in the side view mirror of radius of curvature $R = 2 \; m$. If the jogger is running at a speed of $5 \; m s^{-1}$,how fast does the image of the jogger appear to move when the jogger is $(a) \; 39 \; m$,$(b) \; 29 \; m$,$(c) \; 19 \; m$,and $(d) \; 9 \; m$ away?

Suppose that the lower half of the concave mirror's reflecting surface in the figure is covered with an opaque (non-reflective) material. What effect will this have on the image of an object placed in front of the mirror?

$A$ concave mirror has a focal length $20\,cm$. The distance between the two positions of the object for which the image size is double of the object size is......$cm$

$A$ mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between the object and its image is $40 \ cm$,then the focal length of the mirror is . . . . . . . (in $cm$)