Overview: Reflection of Light: Spherical Mirrors

The diameter of the periphery of the mirror is called the 'aperture' of the mirror.

The point on the principal axis at which light rays parallel to the principal axis, afterreflection from the mirror, actually meet or appear to come from, is called the 'principal focus' of the mirror.

The distance of the principal focus from the pole of the mirror is called the 'focal length' of the mirror.

The plane perpendicular to the principal axis and passing through the principal focus of the mirror is called the ‘focal plane' of the mirror.

Linear magnification produced by a spherical mirror is the ratio of the size of the image to the size of the object, both measured perpendicular to the principal axis.

\[\frac {1}{v}\] + \[\frac {1}{u}\] = \[\frac {1}{f}\]

\[\frac {1}{v}\] + \[\frac {1}{u}\] = \[\frac {1}{f}\]

m = -\[\frac {v}{u}\]

OR

m = -\[\frac {v}{u}\] = \[\frac {f - v}{f}\] = \[\frac {f}{f - u}\].

• For a spherical mirror of small aperture, rays close to the principal axis (paraxial rays) obey the law of reflection accurately.
• In both concave and convex mirrors, using geometrical construction and the law of reflection, the focus lies midway between the pole and the centre of curvature.
• Hence, for a small-aperture spherical mirror, the focal length is half the radius of curvature:
  f = \[\frac {R}{2}\]​

• Parallel ray rule: A ray parallel to the principal axis passes through the focus (concave) or appears to come from the focus (convex) after reflection.
• Focus ray rule: A ray passing through the focus (concave) or directed towards the focus (convex) becomes parallel to the principal axis after reflection.
• Centre of curvature rule: A ray passing through or directed towards the centre of curvature retraces its path after reflection.
• Law of reflection rule: A ray striking the mirror surface reflects according to the laws of reflection.

• Many rays start from an object point, but only two or three rays are sufficient to locate the image.
• In mirrors, reflected rays remain on the same side of the mirror as the object; no real rays exist on the other side.
• If reflected rays actually meet, a real image is formed, which is inverted.
• If reflected rays diverge and meet only on backward extension, a virtual image is formed, which is erect.
• For lenses, real images are formed on the opposite side of the lens and are inverted, while virtual images are formed on the same side as the object and are erect.

• A concave mirror is used for shaving (erect, magnified image).
• Concave (parabolic) mirrors are used in telescopes to observe distant stars.
• Concave mirrors are used in torches, searchlights and headlights to produce a parallel beam.
• Concave mirrors are used by ENT doctors and eye specialists for examination.
• Convex mirrors are used in street lights to illuminate a large area.
• Convex mirrors are used as rear-view mirrors (erect, diminished image, wide view).
• Image identification:
  Erect & same size → Plane mirror
  Erect & magnified → Concave mirror
  Erect & diminished → Convex mirror