Axial magnification = – dv / du = ( v / u ) 2 =( f / f + u ) 2 = ( f-v / f ) 2
Focal Length of a Convex Lens by Displacement Method
Focal length of the convex lens f = ( a 2 – d 2 ) / 4a where , a = distance between the image pin and object pin and d = distance between two positions of lens .
The distance between the two pins should be greater than four times the focal length of the convex lens , i . e ., a > 4f .
Height of the object O = √I 1 I 2
Cutting of a Lens
( i ) If a symmetrical convex lens of focal length f is cut into two parts along its optic axis , then focal length of each part ( a plano convex lens ) is 2f . However , if the two parts are joined as shown in figure , the focal length of combination is again f .
( ii ) If a symmetrical convex lens of focal length f is cut into two parts along the principal axis , then focal length of each part remains unchanged as f . If these two parts are joined with curved ends an one side , focal length of the combination is f / 2 . But on joining two 2 parts in opposite sense the net focal length becomes