Ray optics
Nature of light
Light is a transverse, electromagnetic wave that can be seen by humans. The wave nature of light was first illustrated through experiments on diffraction and interference. Like all electromagnetic waves, light can travel through a vacuum. The transverse nature of light can be demonstrated through polarization.
Light is produced by one of two methods:
Incandescence is the emission of light from “hot” matter (T ≳ 800 K).
Luminescence is the emission of light when excited electrons fall to lower energy levels (in matter that may or may not be “hot”).
Reflection of light
Reflection of light (and other forms of electromagnetic radiation) occurs when the waves encounter a surface or other boundary that does not absorb the energy of the radiation and bounces the waves away from the surface. The simplest example of visible light reflection is the surface of a smooth pool of water, where incident light is reflected in an orderly manner to produce a clear image of the scenery surrounding the pool. Throw a rock into the pool (see Figure 1), and the water is perturbed to form waves, which disrupt the reflection by scattering the reflected light rays in all directions.
The Law of Reflection
When a ray of light strikes a plane mirror, the light ray reflects off the mirror. Reflection involves a change in direction of the light ray. The convention used to express the direction of a light ray is to indicate the angle which the light ray makes with a normal line drawn to the surface of the mirror. The angle of incidence is the angle between this normal line and the incident ray; the angle of reflection is the angle between this normal line and the reflected ray. According to the law of reflection, the angle of incidence equals the angle of reflection.
Reflection from curved surface
Curved mirrors are parts of a sphere. The following terms are used in curved mirrors:
Pole P- it is the centre of the mirror.
Centre of curvature C- it is the centre of the sphere of which the mirror is part.
Radius of curvature r- it is the radius of the sphere of which the mirror is part. Principal axis- it is a line drawn through the pole of the mirror and the centre of curvature.
Principal focus F – for a concave mirror, it is the point at which all rays parallel and close to the principal axis converge at after reflection. In the case of a convex mirror, it is the point at which all rays parallel and close to the principal axis appear to diverge from after reflection. It is also called the focal point.
Focal plane- it is a plane perpendicular to the principal axis and passes through the focal point. It is the plane where parallel rays but not parallel to the principal axis converge at or appear to diverge from after reflection.
Focal length f- it is the distance between the pole of the mirror and its focal point.
When rays are produced behind the mirror, they are indicated using dotted lines. This means that they are imaginary or virtual. Hence the focal point and focal length of a concave mirror are real while the focal point and focal length of a convex mirror arevirtual. A real focal length is given a positive sign while a negative focal length is given a negative sign.
Image formation by plane convex and concave mirror
Image Formation by Convex Mirrors
The definitions of the principal axis, centre of curvature $C$, radius of curvature $R$, and the vertex $V$, of a convex mirror are analogous to the corresponding definitions for a concave mirror. When parallel light-rays strike a convex mirror they are reflected such that they appear to emanate from a single point $F$ located behind the mirror, as shown in Fig. 74. This point is called the virtual focus of the mirror. The focal length $f$ of the mirror is simply the distance between $V$ and $F$. As is easily demonstrated, in the paraxial approximation, the focal length of a convex mirror is half of its radius of curvature.
Image formed by a concave mirror
When the object is placed at infinity, the two rays AB and DE running parallel to the principal axis get reflected at point B and E respectively and intersect each other at the principal focus F on the principal axis. Therefore, in this case the image is formed at the principal focus which is highly diminished, real and inverted.
When the object AB is placed beyond the centre of curvature then a ray of light AD which is parallel to the principal axis and another ray AE which pass through the centre of curvature intersect each other after reflection at point A’ between the focus and centre of curvature. Thus the image formed is between the principal focus F and centre of curvature C, diminished, real and inverted.