For what position of an object, a concave mirror forms a real image equal in size to the object?

A communications satellite in orbit sends a parallel beam of signals down to earth. If these signals obey the same laws of reflection as light and are to be focused onto a small receiving aerial, what should be the best shape of the metal 'dish' used to collect them?

When a spherical mirror is held towards the sun and its sharp image is formed on a piece of carbon paper for some time, a hole is burnt in the carbon paper.

(a) What is the nature of spherical mirror?

(b) Why is a hole burnt in the carbon paper?

(c) At which point of the spherical mirror the carbon paper is placed?

(d) What name is given to the distance between spherical mirror and carbon paper?

(e) What is the advantage of using a carbon paper rather than a white paper?

Where should an object be placed in front of the concave mirror so as to obtain its virtual, erect and magnified image?

For which positions of the object does a concave mirror produce an inverted, magnified and real image?