Which of the following relations about the focal length fo of the objective and focal length fe of the eye piece of a compound is correct?

Analyze the question

This is about the compound microscope. We are asked how the focal length of the objective (fo) compares with that of the eyepiece (fe).

Concept

A compound microscope uses two converging lenses:

• Objective lens: it has a very short focal length. The object is placed just beyond its focal point, so it forms a real, inverted, magnified image.
• Eyepiece lens: it has a longer focal length than the objective, though it is still short. It acts as a magnifying glass on the first image and gives a virtual, further magnified final image.

Magnification of the microscope is approximately:

M ≈ (v/u) × (D/fe)

For the objective to give high magnification, fo must be very small. For the eyepiece, a moderate fe is used. Therefore fo < fe.

Step by step

1. Objective: very short focal length (often a few millimetres), which gives large magnification of a close object.
2. Eyepiece: a slightly longer focal length (a few centimetres).
3. Comparing them: fo < fe.

(Do not confuse this with the astronomical telescope, where the objective has a long focal length and the eyepiece has a short one, so fo > fe.)

Checking the options

• A. fo = fe: incorrect.
• B. fo < fe: correct for a compound microscope.
• C. fo > fe: this is true for a telescope, not a microscope.
• D. fe = 2fo: not a general relation.

Exam tip

Remember: Microscope: objective is the "micro" one (smallest focal length). Telescope: objective is the big, long one. If the question says "compound microscope," think fo < fe.