KinexiaLEARN PHYSICS

Lens Magnification — Cinema Projector (Worked Example)

Easy
Problem

A cinema projector lens sits 10 cm from the film and 300 cm from the screen. What is the magnification of the projected image?

Given

  • do = 10 cm

  • di = 300 cm

Find

The magnification m.

Principle

m = −di/do scales the tiny film frame up to screen size.

Formula

Solution

  1. Note the sign convention: distances are positive on the real side, giving m=−di/dom = -d_i/d_o

  2. Substitute: m=−300/10m = -300/10

  3. Divide: m=−30m = -30

−30 (30× enlarged, inverted)

Unit check

Dimensionless — correct.

What this means physically

−30: a 2 cm film frame becomes a 60 cm... actually a 70 mm frame becomes metres wide. The inversion is corrected by mounting the film upside-down.

Common mistake

Expecting a positive m for a screen image. Screen images are real, and real images from a single lens are inverted — m is negative.