Light and Reflection

We see objects because they reflect light into our eyes. Light travels in straight lines (a straight-line path of light is called a ray). A highly polished surface such as a mirror reflects most of the light falling on it.

You already know the two laws of reflection:

  1. The angle of incidence is equal to the angle of reflection (∠i=∠r\angle i = \angle r).
  2. The incident ray, the normal (at the point of incidence) and the reflected ray all lie in the same plane.

These laws hold for all reflecting surfaces — flat and curved (spherical).

Image in a Plane Mirror

The image formed by a plane mirror has four fixed properties:

  • It is virtual and erect.
  • It is the same size as the object.
  • It is as far behind the mirror as the object is in front of it.
  • It is laterally inverted (left–right reversed).

Curved mirrors, however, form very different images — let's explore spherical mirrors.

Key Point: Plane-mirror image = virtual, erect, same size, laterally inverted.

Spherical Mirrors — Concave and Convex

A spherical mirror has a reflecting surface that is part of a sphere. There are two types:

  • Concave mirror: reflecting surface curved inwards (towards the centre of the sphere). It is a converging mirror.
  • Convex mirror: reflecting surface curved outwards. It is a diverging mirror.

(The back of a spherical mirror is shaded because it does not reflect.)

[Memory Tip] Concave = caves in (inward); convex bulges out.

Important Terms for a Spherical Mirror

Concave and convex mirror terms: pole, centre, focus

Learn these terms — every numerical and diagram uses them:

  • Pole (P): the centre of the mirror's reflecting surface. It lies on the mirror.
  • Centre of curvature (C): the centre of the sphere of which the mirror is a part. It is not on the mirror. (In front of a concave mirror; behind a convex mirror.)
  • Radius of curvature (R): the radius of that sphere; R=PCR = PC.
  • Principal axis: the straight line through the pole P and centre of curvature C. It is normal to the mirror at the pole.
  • Principal focus (F): where rays parallel to the principal axis meet (concave) or appear to come from (convex) after reflection.
  • Focal length (f): the distance PF (pole to focus).
  • Aperture: the diameter of the reflecting surface.

Principal Focus and the R = 2f Relation

Principal focus of concave and convex mirrors

When rays parallel to the principal axis strike a mirror:

  • A concave mirror converges them to a real focus F in front of the mirror.
  • A convex mirror makes them diverge; they appear to come from a virtual focus F behind the mirror.

For mirrors of small aperture, the radius of curvature is twice the focal length: R=2fR = 2f

So the focus lies midway between the pole P and the centre of curvature C.

[Board Trap] If R=20R = 20 cm, then f=R/2=10f = R/2 = 10 cm. This one-line conversion is a guaranteed 1-mark question.

Memory Capsule — Section 1

Quick revision: reflection and spherical mirror terms.

1. Laws of reflection: ∠i=∠r\angle i = \angle r; incident ray, normal, reflected ray in one plane. 2. Plane-mirror image: virtual, erect, same size, laterally inverted. 3. Concave = curved inward (converging); Convex = curved outward (diverging). 4. Terms: P (pole), C (centre of curvature), R (radius), F (focus), f (focal length), principal axis, aperture. 5. R=2fR = 2f → focus midway between P and C. Concave focus is real (front); convex focus is virtual (behind).

Solved Examples

Example 1: NCERT — Radius to Focal Length

The radius of curvature of a spherical mirror is 20 cm. What is its focal length?

Solution: Using R=2fR = 2f: f=R2=20 cm2=10 cmf = \frac{R}{2} = \frac{20\ \text{cm}}{2} = 10\ \text{cm}

The focal length is 10 cm.

Takeaway: Always halve R to get f (and double f to get R).

Example 2: NCERT — Define Principal Focus

Define the principal focus of a concave mirror.

Solution: The principal focus of a concave mirror is the point on the principal axis where rays of light parallel to the principal axis meet (converge) after reflection from the mirror.

Takeaway: For a concave mirror the focus is real; for a convex mirror the parallel rays only appear to come from the focus (virtual).

Example 3: Concave vs Convex

Which spherical mirror converges light and which diverges it? Where is the focus in each?

Solution:

  • A concave mirror converges parallel rays to a real focus in front of the mirror.
  • A convex mirror diverges parallel rays; they appear to come from a virtual focus behind the mirror.

Takeaway: Concave → converging → real focus; Convex → diverging → virtual focus.