Question

Define (i) principal focus of a concave mirror, and (ii) focal length of a concave mirror. Draw a diagram to represent the action of a concave mirror on a beam of parallel light rays. Mark on this diagram principal axis, focus F, centre of curvature C, pole P, and focal length f of the concave mirror.

Answer 1

Hint : The principal focus of a concave mirror is the point where a ray of light parallel to the principal axis will converge to the focal point. The focal length is the distance between the pole of the mirror and the focal point of the mirror.

Complete step by step answer

(i) The principal focus of a concave mirror is a point on its principal axis to which all the light rays which are parallel will converge after reflection from the concave mirror. When an object is placed at infinite distance from the mirror, the rays of light coming from the object will be parallel to the principal axis as shown in the figure. After reflection from a concave mirror, the rays will converge to the focal point of the mirror which is denoted by point F in the image.
(ii) The focal length of a concave mirror is the distance between the pole of the mirror denoted by point P in the image to the focal point of the mirror. Hence it is the distance between points P and F.

Note
For a concave mirror, whose radius of curvature lies in front of the concave mirror, the value is taken negative and so is the focal length of the mirror according to the convention of the Cartesian coordinate system. We must be careful to not mix the focal point and the centre of curvature of the mirror as the centre of curvature is approximately twice the focal length of the mirror.