Ray diagrams for mirrors
The tricky bit isn't the formula — it's drawing the rays. So don't draw them: move the object and watch. Every ray, focus and image here comes from the mirror formula 1/v + 1/u = 1/f with the correct sign convention.
The rules you're seeing
The parallel ray
A ray coming in parallel to the axis reflects through the focus F (concave), or appears to come from F (convex).
The focus ray
A ray heading through F reflects back parallel to the axis. Where two reflected rays meet is the image.
Sign convention
Distances are measured from the pole. Object distance u is negative; f is negative for concave, positive for convex. A negative v means a real image in front.
Magnification
m = −v/u = h′/h. A negative m means the image is inverted (and real); a positive m means erect (and virtual).
Part of the Light — Reflection & Refraction chapter. One of Priodemy for School, free with every EduSuite school.
How to read a mirror ray diagram
What the simulation is actually computing
Nothing here is drawn by hand or approximated. Every frame solves the mirror formula 1/v + 1/u = 1/f for the image distance v, then draws the two standard construction rays to that point. When you drag the object, u changes, v is recomputed, and the rays follow. That is the whole point of the tool: the diagram is a consequence of the formula, not a separate skill you have to memorise alongside it.
For a concave mirror the focal length f is negative and equals half the radius of curvature, so f = R/2. A convex mirror has positive f. Slide the focal length and watch how far the image jumps for a small change — near the focus, the image position is extremely sensitive, which is exactly why a torch bulb sitting slightly off the focus throws a spreading beam instead of a parallel one.
The six cases you are expected to know
Drag the object from far away towards the mirror and you will pass through every case in the Class 10 syllabus, in order. Beyond C the image is real, inverted and diminished, and it sits between F and C. At C the image is real, inverted and the same size, and it lands back at C — the one position where object and image coincide. Between C and F the image is real, inverted and enlarged, and it forms beyond C.
At F the reflected rays come out parallel and never meet, so there is no image at all; the simulator shows the rays diverging to infinity rather than inventing a point. Between F and the pole the image flips to virtual, erect and enlarged, and it appears behind the mirror. A convex mirror only ever gives one case: virtual, erect and diminished, always between P and F, which is why it is used as a rear-view mirror.
What to try
- Park the object exactly at F and watch the image collapse. This is the case students most often get wrong in an exam, because the formula divides by zero rather than returning a number.
- Move the object slowly through C and watch magnification pass through exactly −1.
- Switch to convex and try to produce a real image. You cannot — and seeing that it is impossible is more convincing than being told.
Mistakes that cost marks
Sign convention is where most marks are lost. Distances are measured from the pole, against the direction of the incident light. The object distance u is always negative for a real object. A concave mirror has negative f; a convex mirror has positive f. Substituting a positive u is the single most common error, and it produces an answer that looks reasonable but describes the wrong side of the mirror.
The second trap is reading the sign of v and m as decoration rather than as the answer. A negative v means the image is in front of the mirror and therefore real; a positive v puts it behind and therefore virtual. A negative magnification means inverted, positive means erect. Many questions ask only "what is the nature of the image" — the signs already tell you, with no extra work.