Obtain the lens formula for spherical lens.

Consider the image formation by convex lens as shown in the figure below.

By Cartesian sign convention;

Object distance (OB) = - u;

Image distance (OB’) = + v;

Focal length (OF₂ = OF₂) = f

From the geometry we can see that in the figure above right triangle ΔABO and ΔA’B’O’ are similar.

∴ …… (1)

Also, in figure above by geometry right triangle ΔODF₂ and ΔBAF₂ are similar.

∴

∴ (∵ OD = AB, opposite sides of rectangle ABOD are equal).

∴

∴ ………. (2)

From (1) and (2)

⇒

⇒ .

Dividing each term by uvf, we get.

⇒

⇒

This equation is called the ‘Lens Formula’