# Lens Formula (10th-Physics-Lesson-14. 13)

May 29, 2011

First of all you should revise your knowledge from your previous class book about lenses, its types and formation of image by a lens.

To study the characteristics of an image formed by a lens, an equation can be derived which is called the “lens formula”.

Convex lens formula

Consider fig. 14. 13 where an object OA, is placed in front of a thin convex lens. A ray of light starting from the end point ‘A’ and moving parallel to the principal axis strikes the lens at the point E. after refraction through the lens it passes through the principal focus F. A second ray AC also starting from a passes through the optical centre of the lens and moves straight (undeviated) and intersects the first refracted ray at the point B. thus B is the real image of point A. if this process is repeated for other points of the object OA then a real image iB of the object OA is obtained Generally, the distance of the object from the lens is represented by P and that of image by q. in fig 14. 13 ∆AOC and ∆BIC are similar because <ACO = <BCI. Also one angle in each is 90 degree

Comparing  Eqs. 14. 11 and Eq. 14. 12, we get

Now IC = q, OC = p and CF = F

Or

Dividing both sides by pqf, we get

Equation 14. 13 represents the relation between distance q of the image formed by a convex lens, distance of the object p from the convex lens and its focal length f.

Concave lens formula

Consider fig 14. 14 where an object OA is placed in front of a thin concave lens. A ray of light starting from the end point A and moving parallel to the principal axis strikes the lens at the point E this ray is refracted along ER. A second ray AC also starting from a passes through the optical centre of the lens and is refracted straight along its own path. When the ray RE is produced backwards, it appears to intersect the first ray at the point B. thus B is the virtual image of A. if this process is repeated for the other points of the object OA then the virtual image IB of the object OA is obtained. This image is virtual, erect and diminished. The concave lens formula can be written as:

Since a concave lens always gives virtual image irrespective of the distance of the object from it. Therefore, according to sign conventions, the distance of the virtual image is taken as negative and that of focal length is also taken as negative.

Category: 9th 10th