# Why must both the objective and the eyepiece of a compound microscope have short focal lengths? - Physics

Why must both the objective and the eyepiece of a compound microscope have short focal lengths?

#### Solution

The angular magnification produced by the eyepiece of a compound microscope is [(25/"f"_"e") + 1]

Where,

fe = Focal length of the eyepiece

It can be inferred that if fe is small, then angular magnification of the eyepiece will be large.

The angular magnification of the objective lens of a compound microscope is given as 1/((|"u"_"o"|"f"_"o"))

Where,

uo = Object distance for the objective lens

fo = Focal length of the objective

The magnification is large when uo > fo. In the case of a microscope, the object is kept close to the objective lens. Hence, the object distance is very little. Since uo is small, fo will be even smaller. Therefore, fe and fo are both small in the given condition.

Concept: Optical Instruments - The Microscope
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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 9.26 (d) | Page 347
NCERT Class 12 Physics Textbook
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 32.4 | Page 349

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