Question 42

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

Key idea: cutting a symmetric biconvex lens into two plano-convex halves doubles its focal length.

So,
new objective focal length $$f_o'=2f_o$$

For a compound microscope:

magnification $$M\propto\frac{L}{f_o}$$

To keep magnification same:

$$\frac{L'}{f_o'}=\frac{L}{f_o}$$

$$\frac{L'}{2f_o}=\frac{L}{f_o}\Rightarrow L'=2L$$

final answer:
tube length must be doubled

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