Question

A thin double convex lens of focal length f is broken into 2 equal halves at the axis

Answer 1

The focal length of a lens depend on the extend of convergence it causes..

Incase of a convex lens it has two refractive surfaces…the surface through which ray enter and surface through which it leaves…

But when it is cut into half it becomes plano concave lens and hence the radius of curvature of the planer part is infinity…

Hence convergence doesnt happen at the planar part..and hence effective focal lenth increases ..

In other words a convex lens could be considered as two plano convex lens of focal length f kept together so using formula..

1/f=1/f1 + 1/f2…we get effective focal length f/2..

In reverse if the focal length of convex lens is f.. the focal length of plano convex lens should be 2f…