Lens Magnification — Classroom Projector (Worked Example)

Medium

Problem

A converging projector lens has focal length 10 cm. The slide is 12 cm from the lens. Where is the image, and what is the magnification?

Given

f = 10 cm
dₒ = 12 cm

Find

dᵢ and m.

Principle

The thin-lens equation 1/f = 1/dₒ + 1/dᵢ locates the image; magnification m = −dᵢ/dₒ gives its size and orientation.

Formula

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i};\quad m = -\frac{d_i}{d_o}

1/f = 1/dₒ + 1/dᵢ; m = −dᵢ/dₒ

Solution

Solve for image distance: $1/d_i = 1/10 - 1/12 = (6-5)/60 = 1/60$
So $d_i = 60\ \mathrm{cm}$
Magnification: $m = -60/12 = -5$

dᵢ = 60 cm; m = −5

Unit check

cm throughout; magnification is dimensionless — correct.

What this means physically

The screen must sit 60 cm past the lens, showing an image 5× larger than the slide and upside down (the minus sign) — projectors mount slides inverted to compensate.

Common mistake

Dropping the negative sign and then wondering why the image looks flipped. The sign is information: negative means inverted, positive means upright.