Minimum area of the disc to collect all light

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 \(\text{__________ } \).

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