Reflection at Spherical Mirrors: Formula, Sign Convention and Magnification

Identify mirror type; write signs of u and f; apply 1/v + 1/u = 1/f; solve for v; calculate m = -v/u; use signs of v and m to state image position, nature and size.

Ray diagram should show pole P, principal axis, focus F, centre of curvature C, incident ray parallel to the axis reflecting through F, and ray through C retracing its path. For convex mirror, reflected rays diverge and their backward extensions meet behind the mirror.

For the worked example, a common wrong answer is v = +60 cm and m = +2 because u is wrongly taken as positive.

Reflection at a spherical mirror is the change in direction of light after striking a concave or convex reflecting surface that is part of a sphere, forming images according to the laws of reflection and the mirror formula.

Reflection at a spherical mirror is the change in direction of light after striking a concave or convex reflecting surface that is part of a sphere, forming images according to the laws of reflection and the mirror formula. Mirror formula: 1/v + 1/u = 1/f. Magnification: m = -v/u = image height/object height. Here u, v and f are in metres or centimetres, but all distances must use the same unit. Use this for paraxial rays reflected from spherical mirrors. Concave mirror has f negative in the usual setup; convex mirror has f positive. A concave mirror used in a shaving mirror gives a magnified upright image when the face is placed between the pole and focus. A convex mirror in a vehicle gives a wider field of view with a diminished virtual image.

A spherical mirror has a pole, principal axis, centre of curvature, radius of curvature and focus. For paraxial rays, the object distance u, image distance v and focal length f are related by the mirror formula. Concave mirrors can form real or virtual images depending on object position, while convex mirrors generally form virtual, erect and diminished images for real objects. The Cartesian sign convention is essential: distances measured in the direction of incident light are positive and those opposite are negative. In the usual mirror setup with incident light from left to right, object distance for a real object is negative. Mirror formula: 1/v + 1/u = 1/f. Magnification: m = -v/u = image height/object height. Here u, v and f are in metres or centimetres, but all distances must use the same unit. Use this for paraxial rays reflected from spherical mirrors. Concave mirror has f negative in the usual setup; convex mirror has f positive. A concave mirror has f = -20 cm and an object is placed at u = -30 cm. Using 1/v + 1/u = 1/f: 1/v - 1/30 = -1/20, so 1/v = -1/20 + 1/30 = -1/60. Thus v = -60 cm. Magnification m = -v/u = -(-60)/(-30) = -2. The image is real, inverted and twice the object size. It appears as sign-convention numericals, image nature questions, ray diagram questions, and assertion-reason items on why convex mirrors are used as rear-view mirrors. For the worked example, a common wrong answer is v = +60 cm and m = +2 because u is wrongly taken as positive.