Question

Which of the following statements is incorrect according to the New Cartesian Sign Convention:
(a) Focal length of the concave mirror is positive and that of the convex mirror is negative.
(b) Focal length of concave mirror is negative and that convex mirror is positive.
(c) Image distance is always positive for a concave mirror.
(d) The height of all real and inverted images is positive.

Answer 1

In a concave mirror the focus lies on the left hand side of the mirror and in the convex mirror the focus lies on the right hand side of the mirror.
Quantities on the left of the mirror are taken as positive and those on the right of the mirror are taken to be negative.

Complete step by step answer:
We know, light rays parallel to the principal axis, in the case of a Concave mirror, converge in the direction opposite to the direction of incident light.
This point of convergence on the principal axis is the focus of the mirror.

Since, focus lies on the left hand side of the mirror, it is said to have a real focus, and thus the focal length, which is measured along the principal axis, in the direction of the object are taken to be positive according to the New Sign Convention.
Therefore, the focal length of the concave mirror is positive.

On the other hand, we know, the convex mirror, has a virtual focus, where the light rays, after divergence, meet at a point behind the mirror. This point of divergence, on the right hand side of the mirror, is termed as focus of the convex mirror and since the focal length measured lies away from the object in case of convex mirror and along the direction of incident light, it is taken to be negative.
Therefore, the focal length of the convex mirror is negative.

Thus, option (b) Focal length of concave mirror is negative and that convex mirror is positive, is incorrect.

Note:
Sign Conventions are some laid rules, which helps us in determining the sign of different parameters that are governed while considering different types of mirrors.
It is a choice of physical significance of signs.
It states that all objects are to be kept to the right of the mirror, all distances are to be measured from the pole of the mirror, and the distances measured are taken to be positive, if they are measured opposite to the direction of the incident light, otherwise are taken to be negative if they are along the direction of the incident light.