Physics - Refraction through Lenses and Optical Instruments

A lens is a transparent refracting medium bounded by two surfaces, at least one of which is curved. A convex lens is a converging lens (thicker at the middle), while a concave lens is a diverging lens (thinner at the middle).

Optical Centre ($O$): The point on the principal axis at the centre of the lens. A ray of light passing through $O$ undergoes no deviation.

Principal Focus ($F$): For a convex lens, it is the point where rays parallel to the principal axis actually meet (Real Focus). For a concave lens, it is the point from which they appear to diverge (Virtual Focus).

Focal Length ($f$): The distance between the optical centre and the principal focus. By convention, $f$ is positive for a convex lens and negative for a concave lens.

Rules for Ray Diagrams: (1) A ray parallel to the principal axis passes through (convex) or appears to come from (concave) the focus. (2) A ray passing through the optical centre goes straight. (3) A ray passing through or directed towards the focus emerges parallel to the principal axis.

Nature of Images (Convex Lens): Real and inverted for all positions of object except when the object is between $F_1$ and $O$. When $u < f$, the image is virtual, erect, and magnified.

Nature of Images (Concave Lens): The image formed is always virtual, erect, and diminished, regardless of the position of the object.

Sign Convention (New Cartesian): All distances are measured from the optical centre. Distances in the direction of incident light are positive. Heights above the principal axis are positive.

Magnification ($m$): The ratio of the height of the image ($h_i$) to the height of the object ($h_o$). It is also equal to the ratio of image distance ($v$) to object distance ($u$).

Power of a Lens ($P$): It is the measure of the deviation (convergence or divergence) produced by a lens. It is the reciprocal of the focal length in metres. The S.I. unit is Dioptre ($D$).