KinexiaLEARN PHYSICS

Lens Magnification — Magnifying Glass (Worked Example)

Medium
Problem

A magnifying glass (f = 10 cm) is held 8.0 cm from a stamp. Where is the image, and what is the magnification?

Given

  • f = 10 cm

  • do = 8.0 cm

Find

Image distance di and magnification m.

Principle

First the lens equation locates the image; then m = −di/do gives size and orientation. Object inside f gives a virtual magnified image.

Formula

Solution

  1. Lens equation: 1/di=1/f−1/do=1/10−1/8=−0.0251/d_i = 1/f - 1/d_o = 1/10 - 1/8 = -0.025

  2. So di=−40 cmd_i = -40\ \mathrm{cm} (virtual, same side as object)

  3. Magnification: m=−(−40)/8=+5m = -(-40)/8 = +5

+5 (5× enlarged, upright, virtual)

Unit check

cm ÷ cm — dimensionless, correct.

What this means physically

+5: the stamp appears 5× larger and upright, floating behind the lens — exactly how a magnifier should work. Hold it farther than f and the image flips to real and inverted.

Common mistake

Calling the image real because di 'came out'. Negative di means virtual — the rays only appear to come from behind the lens.