Working difference:
(i) The objective of a telescope forms the image of a very far off object at, or within, the focus of its eyepiece. The microscope does the same for a small object kept just beyond the focus of its objective.
(ii) The final image formed by a telescope is magnified relative to its size as seen by the unaided eye, while the final image formed by a microscope is magnified relative to its absolute size.
(iii) The objective of a telescope has large focal length and large aperture, while the corresponding for a microscope have very small values.
Given: fo = 1.25cm, fe = 5cm
Angular magnification m = 30
Now, m = me × mo
In normal adjustment, the angular magnification of an eyepiece
\(m_e=\frac{d}{f_e}=\frac{25}{5}=5\)
Hence, mo = 6
But mo = \(\frac{v_o}{u_o}⇒-6=\frac{v_o}{u_o}\)
vo = −6uo
Applying lens equation to the objective lens:
\(\frac{1}{f_e}=\frac{1}{v_e}-\frac{1}{u_e}\)
\(\frac{1}{1.25}=\frac{1}{-6u_o}-\frac{1}{u_o}\)
\(\frac{1}{1.25}=\frac{-1-6}{6u_o}=-1.25\times 7\)
\(u_o=\frac{-1.25\times 7}{6}cm\)
uo = −1.46cm