Establish the relation between the radius of curvature R and focal length f of the spherical concave mirror.

Take a concave mirror with centre of curvature C , pole P , focus F and axis C P . From the diagram, we can see that ray A B parallel to axis C P gets reflected along B F direction. The line C B will act as a normal at B . Therefore, from law of reflection ∠ A B C = ∠ C B F ∠ A B C = ∠ B C F From above equations ∠ B C F = ∠ C B F Hence, C F = B F If the mirror is small and point P is very close to point B , then we can assume B F = C F = P F So, C F = P C 2 . In other words, focal length f = R 2

How can you identify a plane, concave and convex mirror by observing image formation?

Plane mirror Concave mirror Convex mirror It produces virtual, erect and same size image behind the mirror. It produces both real and inverted image when the object lies between infinity and focus of the mirror and virtual and erect image is formed when the object lies between focus and pole of the mirror. It produces virtual, erect and diminished image behind the mirror. Magnification of image is always equal to 1 Size of the image increases when the object is brought from infinity to focus. Hence, magnification of image is less than, equal to and greater than 1 Magnification of image is always less than 1