Images Formed by Lenses
Thin converging and diverging lenses form images by refraction. A converging lens brings parallel rays toward a transmitted-side focal point, a diverging lens makes them spread as if from an incident-side focal point, and the thin-lens equation, magnification, and principal-ray diagrams determine image location, type, orientation, and relative size.
Images Formed by Lenses: quick answer
Thin converging and diverging lenses form images by refraction. A converging lens brings parallel rays toward a transmitted-side focal point, a diverging lens makes them spread as if from an incident-side focal point, and the thin-lens equation, magnification, and principal-ray diagrams determine image location, type, orientation, and relative size. Thin-lens imaging uses the same evidence hierarchy as mirrors: first trace where rays or their backward extensions meet, then use the lens equation and magnification to quantify the geometry. Converging and diverging lenses have different focal behavior, but the same consistent sign convention ties rays, equations, and image properties together.
Use the thin-lens approximation with converging and diverging lenses and a consistent sign convention. Determine image properties from the actual rays or their backward extensions rather than from sign memorization alone.
What you should be able to explain and do
Use these as closed-note retrieval prompts before opening the worked examples.
Distinguish converging and diverging thin lenses from their effect on rays parallel to the principal axis.
Construct principal-ray diagrams and classify lens images by type, orientation, and relative size.
Use 1/f=1/s_o+1/s_i and M=−s_i/s_o with a consistent sign convention.
Design or interpret a focal-length experiment using multiple object-image distance pairs and a graph or transformed relationship.
Key terms you need for this lesson
Keep the vocabulary next to the diagram and model so image/angle reasoning never depends on an unexplained term.
converging lens
converging lens is a thin convex lens that brings parallel incident rays toward a focal point on the transmitted side.
diverging lens
diverging lens is a thin concave lens that makes parallel incident rays diverge as if from a focal point on the incident side.
principal axis
principal axis is the reference line through the lens center and focal points.
focal point
focal point is a point associated with parallel-ray convergence or apparent divergence.
real image
real image is an image formed where refracted rays actually intersect.
virtual image
virtual image is an image formed where backward extensions of diverging refracted rays intersect.
magnification
magnification is the signed ratio comparing image and object heights, encoding size and orientation.
Match every expression to its optical geometry and scope
The relationship, variable meanings, conditions, and physical anchor stay together.
| Relationship / model | Variables & units | When to use it | Physical anchor |
|---|---|---|---|
1/f = 1/s_o + 1/s_i | f focal length (m); s_o object distance (m); s_i image distance (m) | thin-lens image calculations with a consistent sign convention | a converging lens with an object beyond f can form a real image on the transmitted side |
M = h_i/h_o = −s_i/s_o | M magnification (dimensionless); h_i image height; h_o object height; s_i image distance; s_o object distance | thin-lens image size and orientation | negative magnification corresponds to an inverted real image under the stated convention |
principal rays locate the image | parallel ray ↔ focal point; central ray passes straight through the thin-lens center; focal ray ↔ parallel ray | constructing ray diagrams for thin converging or diverging lenses | two correctly drawn principal rays are sufficient to locate an image, while a third provides a consistency check |
What a strong optics diagram or graph must show
Draw the optical geometry before doing algebra, then use the diagram as an independent check on signs and image type.
Converging-lens principal rays
parallel → far focal point, center → undeviated in the thin-lens model, near focal point → parallel.
Diverging-lens principal rays
parallel incident ray emerges as if from the near focal point; central ray continues straight; a ray aimed toward the far focal point emerges parallel.
Image classification sketch
actual transmitted-ray intersection means real; backward-extension intersection means virtual.
Reciprocal graph
1/s_i versus 1/s_o follows 1/s_i=1/f−1/s_o, so a linearized graph can expose focal length.
Change one optical condition and inspect what responds
Predict the direction or image type first. Then move one control and reconcile the numerical result with the ray geometry.
Two examples with the model choice exposed
The solution shows why the relationship applies and checks the numerical sign against the ray picture.
Converging lens
Situation: A converging thin lens has f=+0.20 m and an object at s_o=+0.60 m.
Reasoning: 1/s_i=5.00−1.67=3.33 m⁻¹, so s_i=+0.30 m. M=−0.30/0.60=−0.50.
The image is real, inverted, and reduced to half the object height.
Diverging lens
Situation: A diverging thin lens has f=−0.15 m and a real object at s_o=+0.30 m.
Reasoning: 1/s_i=−6.67−3.33=−10.0 m⁻¹, so s_i=−0.10 m. M=−(−0.10)/0.30=+0.33.
The image is virtual, upright, and reduced.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 13.4?
Use the thin-lens model when a converging or diverging lens forms an image and object/image distances or magnification are required.
How this idea fits the course
Lens rays are built from refraction in 13.3; Unit 14 later explains where geometric-ray approximations give way to wave effects.
Scope check before solving
Use the thin-lens approximation with converging and diverging lenses and a consistent sign convention. Determine image properties from the actual rays or their backward extensions rather than from sign memorization alone.
Turn the ray model into measurable evidence
Control the geometry explicitly: a small alignment error changes measured angles and image distances even when the underlying model is correct.
Investigation target
Use a converging thin lens, object, and screen to collect multiple object-image distance pairs and determine focal length from a graph or transformed relationship.
Reasoning errors to eliminate
Repair the ray geometry before doing more arithmetic.
Six things you should be able to do before moving on
Use these as closed-note transfer prompts.
- I can draw the relevant normal, principal axis, focal point, rays, and object/image positions before calculating.
- I can predict reflection/refraction direction or image type from geometry before using an equation.
- I can define every distance, angle, and refractive index I use and keep one sign convention consistent.
- I can distinguish where actual rays meet from where backward extensions meet.
- I can state the topic boundary and know when the ray model must give way to the wave model.
- I can design or critique an optics experiment and justify a claim from measured data and uncertainty.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 13.4 FAQs
What does a converging lens do to parallel rays?
It refracts them toward a focal point on the transmitted side.
What does a diverging lens do to parallel rays?
It makes them diverge as if they originated from a focal point on the incident side.
When is a lens image real?
When the refracted rays actually intersect.
When is a lens image virtual?
When refracted rays diverge and their backward extensions intersect.
Why are there focal points on both sides of a thin lens?
The lens can receive light from either direction; its geometry defines corresponding focal behavior on both sides.
How can focal length be measured experimentally?
Collect several object and image distance pairs and use the thin-lens relationship or a linearized reciprocal graph to infer f.