Geometrical optics

Geometrical optics is branch of optics where light is described by rays. Light rays are conceived as geometrical lines originating from sources, extending though media and being revealed by detectors. The reflection and refraction are the only processes involved in geometrical optics. The geometrical optics fails to explain interference, diffraction and polarisation. .

Optical systems are, in general up made up of a large number of refracting surfaces. In order to obtain the position of the final image due to an optical system, one has to calculate step by step the position of the image due to each surface and consider this image as an object for the next surface. Such a step by step analysis becomes lengthy and tedious. In order to solve such problems easily and more efficiently K. Hallback has introduced matrix method in the study of geometrical optics. The two matrix operations in geometrical optics are known as Refraction matrix & translation matrix.

To know about the optical system, we should describe the cardinal points. They are

(i) Two principal or unit points

(ii)Two focal points.

(iii) Two nodal points

The unit planes are two conjugate planes, one of which lies in object plane and the other in image plane. If a ray strikes the first unit plane (in object side) at a certain height, it emerges out from second unit plane (on the Image dole) at the same height.

Nodal points are a pair of conjugate points on the axis, which have a relative angular magnification of unit. According

to the property of nodal points at a ray striking the first nodal point at an angle of emerges from the second nodal point at the same angle.

Eyepiece is a specially designed which gives a more perfect and magnified image as obtained by a single lens of equal focal length. It consists of two converging lenses separated by certain distance. The lens towards the object is called field lens and other lens towards the eye is called eye lens. It is used in telescopes and microscopes to magnify the image formed by the objective.

The focal lengths of field lens and eye lens and separation between them is such that the chromatic and spherical aberrations are minimum. Spherical aberrations are further reduced by replacing the field lens and eye lens by two plano- convex lenses and the convex side faces the incident beam.

In geometrical optics we will study about two types of path i.e Optical path and geometrical path

When a ray of light travels a distance d in a medium of refractive index n , then the product nd is called optical path.

The basic properties of optical imaging are studied by the first order approximation of ray equation. The result of this is the core of geometrical optics.