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How is the working of a telescope different from that of a microscope? The focal lengths of the objective and eyepiece of a microscope are 1.25 cm and 5 cm respectively. Find the position of the objective lens in order to obtain an angular magnification of 30 in normal adjustment.

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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

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