Converging and diverging lenses: ray diagrams and images: WASSCE Physics

Spectacles, cameras, projectors, microscopes and the lens in your own eye all bend light to form images. A lens is two refracting surfaces working together, and three simple rays tell you where its image will be.

Learning objectives

By the end of this lesson you should be able to:

distinguish converging (convex) and diverging (concave) lenses
define the terms principal axis, optical centre, principal focus and focal length
draw ray diagrams to locate images formed by both kinds of lens
describe the image for different object positions

Types of lens

Converging (convex) lens	Diverging (concave) lens
thicker in the middle than at the edges	thinner in the middle than at the edges
brings parallel rays together at a real focus	spreads parallel rays out, as if from a virtual focus
can form real or virtual images	always forms virtual images
e.g. magnifying glass, camera lens, the eye lens	e.g. spectacles for short sight, door peephole

Terms

Term	Meaning
Optical centre (C)	the centre of the lens; rays through it pass straight on
Principal axis	the line through the optical centre, perpendicular to the lens
Principal focus (F)	for a converging lens, the point where rays parallel to the axis meet after refraction; for a diverging lens, the point from which they appear to diverge
Focal length (f)	the distance from the optical centre to the principal focus

A lens has a principal focus on each side, at equal distances.

Rules for ray diagrams

A ray parallel to the principal axis is refracted through F (converging) or as if from F on the near side (diverging).
A ray through the optical centre passes straight through undeviated.
A ray through F (or heading towards F for a diverging lens) emerges parallel to the axis.

Ray diagram for a converging lens with the object beyond 2F: a ray parallel to the axis passes through F on the far side and a ray through the centre goes straight on; they meet between F and 2F to form a real, inverted, diminished image

Figure 1. Converging lens, object beyond 2F. WASSCE Tutor diagram.

Images formed by a converging lens

Object position	Image position	Nature of image	Application
At infinity	at F	real, inverted, point-sized	burning glass; telescope objective
Beyond 2F	between F and 2F	real, inverted, diminished	camera, the eye
At 2F	at 2F	real, inverted, same size	photocopier
Between 2F and F	beyond 2F	real, inverted, magnified	projector
At F	at infinity	— (parallel beam)	spotlight
Between F and the lens	same side as the object	virtual, upright, magnified	magnifying glass

A convex lens used as a magnifying glass: the object is closer than F, the rays leaving the lens diverge and, traced back, meet behind the object to form a virtual, upright, magnified image

Figure 2. A converging lens as a magnifying glass. WASSCE Tutor diagram.

Images formed by a diverging lens

Ray diagram for a diverging lens: a ray parallel to the axis leaves as if from F on the object side, and a ray through the centre goes straight on; the image is virtual, upright and diminished

Figure 3. A diverging lens always gives a virtual, upright, diminished image. WASSCE Tutor diagram.

For any object position, the image is virtual, upright, diminished, on the same side as the object, between F and the lens.

Common mistake

Real images are formed where rays actually meet and can be caught on a screen; they are always inverted (for a single lens). Virtual images are where rays only appear to come from; they cannot be caught on a screen and are upright. In ray diagrams, draw the extensions of rays to a virtual image as dashed lines.

Finding the focal length roughly (practical)

Focus the image of a distant object (such as a window or a tree across the compound) sharply on a screen with a converging lens. The distance from the lens to the screen is approximately the focal length, because rays from a distant object are almost parallel.

In Sierra Leone

On a sunny afternoon, a hand lens held above a dry leaf focuses sunlight to a tiny bright spot at its focal point; the leaf can start to smoulder. That is why broken bottles left in dry bush can start fires.

Key points

Converging lenses are thicker in the middle and have a real focus; diverging lenses are thinner in the middle with a virtual focus.
Ray rules: parallel → through F; through the centre → straight; through F → parallel.
Converging lens: object beyond F gives a real, inverted image; inside F gives a virtual, upright, magnified image.
Diverging lens: always virtual, upright and diminished.

WASSCE examination focus

WAEC tests this

You will be asked to draw ray diagrams (sometimes to scale on graph paper) to find the position and size of an image, state the nature of the image, and match object positions to instruments (camera, projector, magnifying glass). Use a ruler, arrows on rays, and dashed lines for virtual rays.

Quick check

Where must an object be placed for a converging lens to act as a magnifying glass?
What kind of image does a diverging lens always form?
Which instrument uses an object placed between F and 2F of a converging lens?

Answers: 1. Between the lens and its principal focus. 2. Virtual, upright and diminished. 3. A projector.

Converging and diverging lenses: ray diagrams and images