AP Syllabus focus: 'Three principal rays determine mirror images, including the image location, type, size, and orientation: upright or inverted, real or virtual, reduced, enlarged, or same size.'
Mirror ray diagrams give a visual method for predicting image formation in curved mirrors. By tracing only a few carefully chosen rays, you can determine where an image appears and describe its properties.
What Mirror Ray Diagrams Show
A mirror ray diagram represents light leaving one point on an object and reflecting from a mirror. In practice, the top of the object is usually chosen, because the bottom often lies on the axis and is easier to infer later. The image is found by locating where the reflected rays meet, or seem to meet.
Most mirror ray diagrams are organized around the principal axis.
Principal axis: A straight reference line that passes through the center of a spherical mirror and is used to draw and interpret mirror ray diagrams.
The object is usually drawn as an upright arrow. Rays are drawn with straight lines and arrowheads to show the direction of travel. For a curved mirror, the geometry is simplified by using three special rays whose behavior is easy to predict.
Side-by-side ray diagrams for concave and convex spherical mirrors using principal rays from the object tip. The concave case shows reflected rays physically intersecting to form a real (inverted) image, while the convex case uses dashed backward extensions to locate a virtual (upright) image behind the mirror. Labels for the principal axis, focal point , and center of curvature make the construction rules explicit. Source
The Three Principal Rays
Concave mirror rays
For a concave mirror, the principal rays are chosen because their reflections follow simple, repeatable paths.
A ray drawn parallel to the principal axis reflects through the focal point.
A ray drawn through the focal point reflects parallel to the principal axis.
A ray drawn through the center of curvature reflects back along its own path.
These three rays all start from the same point on the object, usually the tip.
A concave-mirror ray diagram drawn from the tip of the object using three easy-to-sketch principal rays. The reflected rays converge at a single point, identifying the top of a real image and making the “intersection of reflected rays” rule visually unambiguous. The diagram’s uncluttered geometry helps students practice accurate construction with a straightedge. Source
If they are drawn correctly, they intersect at one point after reflection. That intersection gives the corresponding point on the image.
Convex mirror rays
For a convex mirror, the reflected rays spread apart, so the image is found by extending the rays backward behind the mirror.
A ray drawn parallel to the principal axis reflects as if it came from the focal point behind the mirror.
A ray drawn toward the focal point behind the mirror reflects parallel to the principal axis.
A ray drawn toward the center of curvature behind the mirror reflects back on itself.
Because the rays diverge after reflection, dashed lines are used behind the mirror to show their backward extensions.
A convex-mirror reference sheet emphasizing that and lie behind the mirror and that reflected rays must be extended backward (dashed) to locate the virtual image. It highlights the standard convex-mirror outcome—virtual, upright, reduced—while reinforcing the two-ray construction procedure used in AP-style diagrams. The labeling helps prevent the common error of treating dashed extensions as real rays. Source
The apparent intersection of those dashed lines gives the image location.
How to Construct a Mirror Ray Diagram
A clear method helps prevent mistakes.
Draw the mirror, the principal axis, and the object.
Start the rays from the top of the object.
Choose any two principal rays. Two are enough to locate the image; the third is used as a check.
Draw the reflected rays carefully with a ruler.
If the reflected rays meet in front of the mirror, place the top of the image at that intersection.
If the reflected rays do not meet, extend them backward with dashed lines. Where the dashed lines meet is the top of the image.
Draw the rest of the image from that point down to the principal axis.
The image is not found by guessing from the mirror shape alone. It must come from the geometric intersection of rays or of their extensions.
Determining Image Properties
Once the image has been located, the ray diagram also shows its main properties.
If the reflected rays actually cross, the image is real.
Real image: An image formed where reflected rays actually intersect, so light is physically present at the image location.
A real image in a mirror diagram is drawn on the same side of the mirror as the object. In standard curved-mirror diagrams, it is usually inverted, meaning the image arrow points downward relative to the axis.
If the rays spread apart and only their backward extensions meet, the image is virtual.
Virtual image: An image formed where reflected rays do not actually meet, but appear to originate when the rays are extended backward.
A virtual image is drawn behind the mirror. In mirror ray diagrams, it is usually upright, meaning the image arrow points upward like the object.
The diagram also shows size:
Enlarged means the image arrow is taller than the object arrow.
Reduced means the image arrow is shorter than the object arrow.
Same size means the image and object arrows have equal height.
These judgments come directly from the completed diagram, not from memorizing isolated rules.
Recognizing Common Image Patterns
A ray diagram makes the image behavior visually clear.
For a concave mirror, reflected rays may actually converge or may diverge after reflection, depending on how the object is placed. That is why a concave mirror can produce either a real inverted image or a virtual upright image.
For a convex mirror, reflected rays always diverge, so the image is always found from backward extensions. This leads to a virtual, upright, reduced image.
The power of the ray diagram is that these outcomes are seen from the rays themselves.
Common Drawing Errors to Avoid
Small drawing errors can lead to a wrong image.
Mixing up a solid reflected ray with a dashed extension.
Drawing rays from different points on the object instead of from the same point.
Forgetting that the third principal ray is a check, not a different image.
Placing the image where lines merely cross on the page without considering whether those lines represent actual rays or extensions.
Making the diagram so rough that size or orientation cannot be judged.
A neat, consistent diagram is essential. In AP Physics 2 Algebra, the goal is not artistic detail but correct geometry and correct interpretation of the image.
FAQ
Any ray from a point on the object will obey the law of reflection and contribute to the image. In that sense, principal rays are not the only possible rays.
They are used because their paths are easy to predict from the mirror geometry. That makes diagrams faster, clearer, and more reliable on an exam.
This usually means the drawing is slightly inaccurate rather than the physics being wrong. Pencil thickness, poor ruler placement, or a diagram that is not drawn to scale can all cause small mismatches.
Use the point of closest intersection as the image location, then check whether all rays started from the same object point and followed the correct reflection rule.
The bottom of the object is often placed directly on the principal axis, so its image point will also lie on the axis. That means it does not need much construction.
Tracing rays from the top gives the full image height and makes the orientation easy to identify at a glance.
At the point where that ray hits the mirror, it travels along the local normal to the surface. That makes the angle of incidence zero.
Since the angle of reflection equals the angle of incidence, the reflected ray must return along the same line.
A qualitative diagram is mainly for identifying the general image properties, such as real versus virtual or upright versus inverted. Exact distances are not trusted unless the diagram is carefully scaled.
A to-scale diagram is drawn with measured distances and a consistent geometry, so the image position and relative size can be estimated more precisely.
Practice Questions
A student draws a ray diagram for an object in front of a convex mirror. After reflection, the rays diverge, but their dashed backward extensions meet behind the mirror. State the image type and orientation.
[2 marks]
1 mark: States that the image is virtual.
1 mark: States that the image is upright.
Describe how to use principal rays from the top of an object to locate the image formed by a concave mirror. Your answer should explain how the diagram reveals whether the image is real or virtual, upright or inverted, and enlarged or reduced.
[5 marks]
1 mark: Describes or draws a ray parallel to the principal axis that reflects through the focal point.
1 mark: Describes or draws a second valid principal ray, either through the focal point and then parallel to the axis, or through the center of curvature and back on itself.
1 mark: States that the image location is found where the reflected rays intersect, or where their backward extensions intersect if needed.
1 mark: Correctly states that an actual intersection gives a real image, while an apparent intersection from extensions gives a virtual image.
1 mark: Explains that orientation comes from whether the image is above or below the axis, and size comes from comparing image height with object height.
