Images Formed by Mirrors
Plane, concave spherical, and convex spherical mirrors form images according to ray geometry. Concave mirrors converge parallel rays toward a focal point, convex mirrors make parallel rays diverge as if from a focal point behind the mirror, and image location and magnification can be found with ray diagrams and the mirror equation using one consistent sign convention.
Images Formed by Mirrors: quick answer
Plane, concave spherical, and convex spherical mirrors form images according to ray geometry. Concave mirrors converge parallel rays toward a focal point, convex mirrors make parallel rays diverge as if from a focal point behind the mirror, and image location and magnification can be found with ray diagrams and the mirror equation using one consistent sign convention. Mirror questions become reliable when ray geometry and sign convention agree. A real image is where reflected rays actually meet; a virtual image is where their backward extensions appear to meet. The equation then quantifies a geometry that the ray diagram should already make plausible.
Limit mirror analysis to plane mirrors and concave or convex spherical mirrors. Use one sign convention consistently and support image type, orientation, and size with ray geometry rather than memorized sign rules alone.
What you should be able to explain and do
Use these as closed-note retrieval prompts before opening the worked examples.
Distinguish plane, concave spherical, and convex spherical mirrors and their focal behavior.
Use principal rays to locate mirror images and classify them as real/virtual, upright/inverted, and enlarged/reduced/same size.
Use 1/f=1/s_o+1/s_i and M=−s_i/s_o consistently with a stated sign convention.
Relate spherical-mirror focal length and radius of curvature with f=R/2.
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.
principal axis
principal axis is the reference line through the mirror vertex and center of curvature.
focal point
focal point is the point toward which reflected parallel rays converge or from which they appear to diverge.
concave mirror
concave mirror is a converging spherical mirror whose reflective surface curves inward.
convex mirror
convex mirror is a diverging spherical mirror whose reflective surface bulges outward.
real image
real image is an image formed where reflected rays actually intersect.
virtual image
virtual image is an image formed where backward extensions of diverging reflected rays intersect.
magnification
magnification is a signed ratio describing image size and orientation relative to the object.
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) | plane or spherical-mirror image calculations with a consistent sign convention | a concave mirror with an object beyond its focal point can produce a positive real-image distance |
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 | mirror image size and orientation | negative M represents an inverted image under the stated sign convention |
f = R/2 for a spherical mirror | f focal length (m); R signed radius of curvature (m) | concave or convex spherical mirrors in the geometric/paraxial model | a concave spherical mirror with R=40 cm has |f|=20 cm |
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.
Principal-ray diagram
include the principal axis, mirror, focal point, object, and at least two correctly constructed rays.
Concave image map
object beyond f can form real inverted images; object inside f forms a virtual upright enlarged image.
Convex image map
reflected rays diverge and their backward extensions form an upright reduced virtual image behind the mirror.
Plane-mirror geometry
image distance behind the mirror equals object distance in front; image is upright, virtual, and the same size.
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.
Concave mirror image
Situation: A concave mirror has f=+0.20 m and an object at s_o=+0.60 m.
Reasoning: 1/s_i=1/f−1/s_o=5.00−1.67=3.33 m⁻¹, so s_i=+0.30 m. Then M=−0.30/0.60=−0.50.
The image is real, inverted, and half the object height.
Plane mirror image
Situation: An object is 0.40 m in front of a plane mirror.
Reasoning: For a plane mirror f is effectively infinite, so 1/f=0 and the mirror equation gives s_i=−s_o. Magnification is +1.
The virtual image is 0.40 m behind the mirror, upright, and the same size.
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 13.2?
Use spherical-mirror imaging when object position, focal length, image location, orientation, or magnification are being related.
How this idea fits the course
The ray-diagram habits developed here transfer directly to thin lenses in 13.4, while 13.1 supplies the reflection law.
Scope check before solving
Limit mirror analysis to plane mirrors and concave or convex spherical mirrors. Use one sign convention consistently and support image type, orientation, and size with ray geometry rather than memorized sign rules 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 concave spherical mirror and screen to measure image distance for several object distances and estimate focal length from transformed data and ray geometry.
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 13.2 FAQs
What mirrors are in scope?
Plane mirrors plus concave and convex spherical mirrors.
What makes a mirror image real?
The reflected rays themselves intersect at the image location.
What makes an image virtual?
The reflected rays diverge, but their backward extensions intersect at the apparent image location.
What does negative magnification mean in the convention used here?
The image is inverted relative to the object.
What is special about a plane mirror?
Its focal point is effectively at infinity; image and object distances have equal magnitudes and the image is upright, virtual, and same size.
How many principal rays do I need?
Two correctly drawn independent principal rays locate the image; a third can check consistency.