Lens Magnification — Telescope Objective (Worked Example)

Medium

Problem

A telescope objective lens forms an image of a distant ridge 0.50 m behind the lens when the ridge is effectively 10 m away in this tabletop model. What is the magnification?

Given

do = 10 m
di = 0.50 m

Find

The magnification m.

Principle

For distant objects di ≈ f; m = −di/do is tiny — telescopes magnify angular size via the eyepiece, not this linear m.

Formula

m = -\frac{d_i}{d_o}

m = −di/do

Solution

Note: for distant objects the image forms near the focal point, so $d_i$ is small while $d_o$ is large
Substitute: $m = -0.50/10$
Divide: $m = -0.05$

−0.05 (20× reduced, inverted)

Unit check

Dimensionless — correct.

What this means physically

−0.05: the objective actually shrinks the scene — its job is to gather light and make a bright real image for the eyepiece to magnify angularly. Telescope 'magnification' (e.g. 100×) is angular, a different quantity.

Common mistake

Confusing linear and angular magnification. A telescope objective's linear m is < 1; the quoted 100× is angular magnification from the eyepiece.