Waves & Optics · 05 / 06

Lenses & Imaging

A lens redirects many rays from each object point. Where those rays converge—or appear to diverge from—determines the image position, orientation, and size.

The learner question

How can curved glass create an image somewhere else in space?

Each small region of the lens refracts light. The lens shape organizes those direction changes so rays from one object point either meet again or leave with directions that appear to come from a common point.

Thin-lens relationships
1f=1do+1di\frac1f=\frac1{d_o}+\frac1{d_i}
m=dido=hihom=-\frac{d_i}{d_o}=\frac{h_i}{h_o}

This page uses a converging thin lens and the usual real-is-positive sign convention for image distance.

Ray-construction lab

Move the object through the focal region.

real image
FF
dₒ
3.50 m
dᵢ
4.67 m
magnification
-1.33
image
real, inverted
Focal length f2.00 m
Object distance dₒ3.50 m
Object height hₒ1.00 m
imaging idea
Outside the focal length

For a converging lens with dₒ > f, outgoing rays can actually meet on the far side, producing a real inverted image.

imaging idea
Inside the focal length

When dₒ < f, outgoing rays diverge. Tracing them backward produces an upright virtual image on the object side—the magnifying-glass regime.

imaging idea
Principal rays are construction shortcuts

The familiar parallel, focal, and central rays are selected representatives of a much larger family of refracted rays from the same object point.

At dₒ = f

The outgoing rays are parallel in the ideal thin-lens model, so the image is described as being at infinity.

Magnification includes orientation

Negative magnification means the image is inverted relative to the object; positive magnification means upright.

Imaging is reversible

Light paths through passive optical systems are reversible, so object and image roles can often be exchanged geometrically.

Transfer check

An object is placed inside the focal length of a converging lens. What kind of image appears?

← Diffraction
Next: Standing Waves & Resonance · planned