A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

Step-by-step solution

Focal length of the objective after cutting: For a symmetric biconvex lens with both radii of magnitude R : 1 f_o = ( - 1) ( 1 R - 1 -R ) = 2( - 1) R When the lens is cut vertically (perpendicular to the principal axis), each half becomes a plano-convex lens with one flat surface: 1 f_o' = ( - 1) ( 1 R - 0 ) = - 1 R Comparing the two: f_o' = 2f_o , so the focal length of the objective doubles. Magnification of a compound microscope: M L f_o D f_e where L is the tube length, f_o is the objective focal length, f_e is