2. Reflection of Light

When light travelling through one medium strikes a smooth surface and bounces back into the same medium, this phenomenon is called reflection. Reflection allows us to see objects that do not emit their own light — we see them because light from a source bounces off their surface and enters our eyes.

2.1 Laws of Reflection

Reflection of light, whether from a plane surface or a curved surface, always obeys two fundamental laws:

1. The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
2. The angle of incidence is always equal to the angle of reflection (∠i = ∠r), both angles being measured from the normal, not from the surface itself.

The normal is an imaginary line drawn perpendicular to the reflecting surface at the point where the incident ray strikes it. These two laws hold true for all types of mirrors — plane, concave, and convex — and indeed for reflection of any wave, not just light.

2.2 Plane Mirrors

A plane mirror is a flat, polished reflecting surface. When an object is placed in front of a plane mirror, the image formed has the following characteristics, all of which are commonly tested:

• The image is virtual (cannot be caught on a screen) and erect (upright).
• The image is of the same size as the object (lateral magnification = 1).
• The image is formed as far behind the mirror as the object is in front of it (image distance = object distance).
• The image is laterally inverted — that is, left appears as right and right appears as left. This is why the word 'AMBULANCE' is often printed in mirror-writing on the front of ambulances, so that drivers ahead can read it correctly in their rear-view mirrors.

If two plane mirrors are inclined to each other at an angle θ, the number of images formed of an object placed between them is given by (360°/θ) − 1, provided 360°/θ is a whole number. When two mirrors are placed parallel to each other (θ = 0°), an infinite number of images are formed, as seen in a barber's shop or a kaleidoscope.

A ray diagram for a plane mirror can be understood simply by extending each reflected ray backwards, behind the mirror, until the extended (dashed) lines meet; that meeting point is where the virtual image appears to be located. Because no actual light rays pass through this point behind the mirror, the image cannot be captured on a screen — this is precisely what makes an image 'virtual' as opposed to 'real'. The everyday device built on this principle is the kaleidoscope, a tube containing two or three mirrors inclined to one another along with loose coloured beads or glass pieces at one end; multiple reflections between the mirrors create the intricate, symmetric patterns seen when looking through it.

2.3 Spherical Mirrors

A spherical mirror is a mirror whose reflecting surface is a part cut out of a hollow sphere. There are two types:

Concave mirror: The reflecting surface is curved inward, like the inside of a spoon. It converges parallel rays of light to a point, and is therefore also called a converging mirror.

Convex mirror: The reflecting surface bulges outward, like the outside of a spoon. It spreads out (diverges) parallel rays of light, and is therefore also called a diverging mirror.

Important terms in spherical mirrors

• Pole (P): the centre point of the mirror's reflecting surface.
• Centre of curvature (C): the centre of the hollow sphere of which the mirror is a part.
• Radius of curvature (R): the radius of that sphere; distance between pole and centre of curvature.
• Principal axis: the straight line passing through the pole and the centre of curvature.
• Focus/Focal point (F): the point on the principal axis where parallel rays converge (concave) or appear to diverge from (convex) after reflection.
• Focal length (f): the distance between the pole and the focus. It is related to the radius of curvature by f = R/2.

Image formation by a concave mirror

The nature, size, and position of the image formed by a concave mirror depend entirely on where the object is placed relative to the pole, focus, and centre of curvature. This is usually summarised as follows (as would be traced out with ray diagrams using two of the standard rays: a ray parallel to the principal axis that reflects through the focus, a ray through the focus that reflects parallel to the axis, and a ray through the centre of curvature that reflects back along itself):

Note the important special case: when an object is placed between the pole and the focus of a concave mirror, the image behaves like that of a plane mirror in being virtual and erect, but unlike a plane mirror the image is magnified — this is the principle used in a shaving/make-up mirror.

Ray diagrams for spherical mirrors are conventionally drawn using any two of three especially simple, predictable rays, since the point where any two of them intersect (after reflection) locates the image. A ray travelling parallel to the principal axis, after striking a concave mirror, reflects back through the principal focus (and, for a convex mirror, reflects such that it appears to diverge from the focus behind the mirror). A ray passing through (or, for a convex mirror, directed towards) the focus is reflected parallel to the principal axis after striking the mirror. A ray passing through (or directed towards) the centre of curvature strikes the mirror along the normal and is reflected straight back along its own path, since the normal at any point on a spherical mirror always passes through the centre of curvature. A fourth ray, striking the pole of the mirror, is reflected such that the angle of incidence equals the angle of reflection with respect to the principal axis itself, which acts as the normal at the pole. Wherever the two chosen reflected rays actually cross, a real image is formed there and can be captured on a screen; wherever their backward extensions cross (behind the mirror), a virtual image is formed and can only be seen by looking into the mirror, never projected onto a screen.

Image formation by a convex mirror

A convex mirror always produces an image that is virtual, erect, and diminished (smaller than the object), regardless of the object's distance from the mirror. As the object is moved away from the mirror, the image also moves away from the pole (toward the focus) and continues to shrink, but it never becomes real or inverted. This single, unchanging behaviour makes convex mirrors especially useful for safety and surveillance applications, discussed below.

Mirror formula and magnification

For all spherical mirrors, whether concave or convex, the relationship between object distance (u), image distance (v), and focal length (f) is given by the mirror formula:

Linear magnification (m), which tells us how many times larger or smaller the image is compared to the object, is given by:

m = height of image / height of object = −v/u

A negative value of magnification indicates a real and inverted image, while a positive value indicates a virtual and erect image, according to the Cartesian sign convention explained in the reference table near the end of these notes. If |m| > 1 the image is magnified; if |m| < 1 it is diminished; if |m| = 1 the image is the same size as the object.

Uses of concave and convex mirrors