Reflection of Light and Spherical Mirrors

Introduction — Why We See the World

A mirror on the wall, a shiny spoon, ripples glinting on a pond — all show us that light bounces back from surfaces it meets. This bouncing is called reflection. Because our eyes cannot create light, we see an object only when light from it (either produced by or reflected from it) enters our eyes. Chapter 9 opens the physics of light with two great ideas — reflection (this part and Part 2) and refraction (Part 3).

9.1 Reflection of Light

When a ray of light meets a polished surface like a plane mirror, almost all of it is thrown back. The ray that strikes the surface is the incident ray; the one that leaves is the reflected ray. A line drawn perpendicular to the mirror at the point of incidence is called the normal.

9.1.1 Image Formed by a Plane Mirror

A plane mirror produces an image with the following properties:

• The image is virtual (cannot be caught on a screen) and erect.
• Image size is the same as the object size.
• The image is as far behind the mirror as the object is in front of it.
• It is laterally inverted — the left of the object appears as the right of the image.

9.1.2 Regular vs Irregular (Diffuse) Reflection

When parallel rays strike a smooth, polished surface (mirror, still water) they all reflect in one direction — this is regular reflection, and it produces clear images. When the same parallel rays fall on a rough surface (a wall, a page, cloth) the tiny bumps send each ray off in a different direction — this is irregular or diffuse reflection, and it does not form an image but allows us to see the object from every direction.

9.2 Spherical Mirrors

A mirror whose reflecting surface is part of a hollow sphere is called a spherical mirror. There are two kinds:

• Concave mirror — the reflecting side is the inside (bowl-like) surface. It converges light.
• Convex mirror — the reflecting side is the outside (bulging) surface. It diverges light.

9.2.1 Key Terms of a Spherical Mirror

• Pole (P): the centre of the reflecting surface.
• Centre of curvature (C): the centre of the sphere of which the mirror is a part. For a concave mirror C is in front of the mirror; for a convex mirror C lies behind it.
• Radius of curvature (R): the distance PC — the radius of the parent sphere.
• Principal axis: the straight line through P and C.
• Principal focus (F): the point on the principal axis where rays parallel and close to the axis, after reflection, actually meet (concave) or appear to come from (convex).
• Focal length (f): distance PF.
• Aperture: the effective diameter of the reflecting surface. We assume "small aperture" so that mirror formula holds accurately.

9.2.2 New Cartesian Sign Convention

To use one formula for every case, we fix directions. In the New Cartesian sign convention:

• The pole (P) is the origin.
• The principal axis is taken as the x-axis.
• The object is always placed on the left of the mirror and light travels from left to right. So the incident direction is positive.
• Distances measured against the incident direction (i.e. to the left of P) are negative; distances measured along the incident direction (to the right of P, i.e. behind the mirror) are positive.
• Heights above the principal axis are positive; heights below are negative.

9.3 Image Formation by Concave Mirrors — Six Cases

To draw a ray diagram we use two of these four standard rays:

1. A ray parallel to the principal axis passes through F after reflection.
2. A ray passing through F emerges parallel to the principal axis after reflection.
3. A ray passing through C strikes the mirror normally and retraces its path.
4. A ray striking the pole is reflected making equal angles with the principal axis.

Case 1 — Object at infinity

Parallel rays from a very distant object (like the Sun) converge at F. Image is real, inverted, highly diminished (point-sized), formed at F.

Case 2 — Object beyond C

Image forms between F and C. It is real, inverted, diminished.

Case 3 — Object at C

Image at C; real, inverted, same size as object.

Case 4 — Object between C and F

Image forms beyond C; real, inverted, enlarged. (Used in movie projectors.)

Case 5 — Object at F

Reflected rays are parallel — image is formed at infinity, highly enlarged, real, inverted. (Used in torches and searchlights, which need a parallel beam.)

Case 6 — Object between P and F

The reflected rays diverge. When extended behind the mirror they appear to meet, forming a virtual, erect, enlarged image behind the mirror. (Used as a shaving mirror, in dentist's mirrors and make-up mirrors.)

9.4 Image Formation by a Convex Mirror

A convex mirror always produces a virtual, erect, diminished image behind the mirror — for every position of the object from very close to very far. This is why it has a wide field of view.

9.5 Uses of Spherical Mirrors

• Concave mirrors — shaving mirrors (object between P and F gives an enlarged erect image); dentists' and ENT mirrors; reflectors in torches, headlights and searchlights (source at F gives a parallel beam); solar furnaces and solar cookers (parallel rays from Sun focus at F to produce intense heat).
• Convex mirrors — rear-view (wing) mirrors of vehicles, because they always give an erect, diminished image with a wider field of view than a plane mirror of the same size. Used as security mirrors at blind corners and in shops.