A concave mirror of radius of curvature (R) has a circular outline of radius (r). A circular disc is to be placed normal to the axis at the focus so that it collects all the light that is reflected from the mirror from a beam parallel to the axis.for (r << R). The area of the disc has to be atleast----
Answers
This is not very clear. The best way to start is with a diagram (the questioner ought to have included one) and identifying what assumptions need to be made.
It seems to me that the disc will obstruct some of the light. Light close to the axis (paraxial rays) is focussed to a point at F. However, this light is blocked by the disk. Light further from the axis comes to a focus closer to the mirror than F. If the disk is not big enough it will not strike the disk at all.
So I think you have to concentrate on what happens to rays which strike the mirror at the rim (P), which is at height FT=h from the axis. Use geometry (i=r) to work out how far from the axis such rays will be when they cross a plane at F=R/2 after reflection, striking the plane at Q. In the diagram CP=R, the radius of the spherical mirror.