Lesson 1 of 11 · 7 min

Reflection by spherical mirrors and the sign convention

NCERT § "Reflection of Light by Spherical Mirrors"

Kabir's shaving mirror makes his face look huge up close, yet a car's side mirror makes the traffic behind look small. Both are just curved pieces of a sphere.

The story this chapter follows: Kabir's optics kit

Kabir has a small kit on his desk: a candle flame 2 cm tall, a biconvex glass lens (n = 1.5, both faces of radius 10 cm, so f = +10 cm), a concave shaving mirror of focal length 10 cm, and a glass of water (n = 4/3). Every image in this chapter is one he can make on that desk, and every number comes from those four things.

The lesson in notes

In short

Laws of reflection: the angle of reflection equals the angle of incidence, and the incident ray, the reflected ray and the normal at the point of incidence are coplanar. For a curved mirror the normal is along the radius at that point.

NCERT uses the Cartesian sign convention: every distance is measured along the principal axis, taking the pole of the mirror (or, for a lens, its optical centre) as the origin.

Distances measured in the direction of the incident light are positive; those measured against it are negative. Heights above the principal axis are positive and below it negative.

With light coming from the left, a real object in front of a mirror has negative u; a concave mirror has negative f and R, and a convex mirror has positive f and R.

For a spherical mirror of small aperture using paraxial rays, the focal length is half the radius of curvature: f = R/2.

Paraxial rays are rays close to the principal axis making small angles with it; the simple mirror and lens formulas are valid only for them.