Consider Lens Makers formula
From Eqs. (1) and (3), we get
where BO = u and DI = v
Applying sign convention, for convex lens, we write, 1/u + 1/v = 1/f
Applying sign convention, for concave lens, we write 1/v - 1/u = 1/f
Which is lens formula for thin lens.
To find the image of an object by a lens, we can, in principle, take any two rays emanating from a point on an object; trace their paths using the laws of refraction and find the point where the refracted rays meet (or appear to meet). In practice, however, it is convenient to choose any two of the following rays:
(i) A ray emanating from the object parallel to the principal axis of the lens after refraction passes through the second principal focus F′ (in a convex lens) or appears to diverge (in a concave lens) from the first principal focus F.
(ii) A ray of light, passing through the optical centre of the lens, emerges without any deviation after refraction.
(iii) A ray of light passing through the first principal focus (for a convex lens) or appearing to meet at it (for a concave lens) emerges parallel to the principal axis after refraction.
