Question

Two points $P$ and $Q$ lie on either side of an axis $XY$ as shown. It is desired to produce an image of $P$ at $Q$ using a spherical mirror, with $XY$ as the optic axis. The mirror must be

• A. Converging and positioned to the left of $P$ .
• B. Diverging and positioned to the left of $P$ .
• C. Converging and positioned to the right of $Q$ .
• D. Diverging and positioned to the right of $Q$ .

Answer 1

Answer: (A)

It is clear from the diagram given in the question that we need to produce an inverted image of the object (Since P and Q are on the opposite side of the principal axis). hence the image should be real because only a real image can be inverted. We can also see that the distance of point Q from the principal axis is more than the distance of P from the principal axis. This means the image is also magnified. So we conclude that the spherical mirror should be able to produce a real, inverted and magnified image of the object. This can be only achieved by a concave mirror by placing the object between principal focus and centre of curvature and the image will be formed beyond the centre of curvature. The required diagram is given below.