A compound microscope is designed with two symmetric biconvex lenses

Question

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 ______. [2026]

Smart Achievers · Accepted Answer

(1)

$M = \frac{L}{F_{0}} \frac{D}{F_{e}}$

$\frac{1}{F_{0}} = (n - 1) (\frac{2}{R})$

$But when cut$

$\frac{1}{F_{0}'} = (n - 1) (\frac{1}{R}) = \frac{1}{2 F_{0}}$

$So, \frac{L}{F_{0}} = \frac{L'}{F_{0}'} = 2 L$

Solution

1 increased two times

2 increased $\frac{3}{2}$ times

3 decreased two times

4 decreased $\frac{3}{2}$ times

Ans.
(1)

$M = \frac{L}{F_{0}} \frac{D}{F_{e}}$

$\frac{1}{F_{0}} = (n - 1) (\frac{2}{R})$

$But when cut$

$\frac{1}{F_{0}'} = (n - 1) (\frac{1}{R}) = \frac{1}{2 F_{0}}$

$So, \frac{L}{F_{0}} = \frac{L'}{F_{0}'} = 2 L$

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