The Thin Lens Formula

The nature and position of an image formed by a lens can be calculated from the lens formula.

Here p is the distance of object from the lens and q is the distance of image from the lens and f is the focal length of the lens.  

a

      Let us consider an object OP whose real but inverted image is formed by a thin convex lens as shown in the figure:

 It is clear from the figure that ∆OXP and ∆IXQ are similar then according to theorem of geometry,

                                          

                                           

In figure, ∆AFX and ∆IFQ are also similar then according to geometry,

                                                    

                                      

Comparing equation(1) and (2),

                                                  

                                                  
                                                  
Or,

This equation is known as the lens formula.