← Lenses and images

Evaluate a flawed ray diagram

Thora checks a classmate's lens diagram before a quiz. The image arrow sits in a believable spot, but something feels off: the ray through the middle of the lens has a kink in it.

A finished diagram can look tidy and still be wrong. The test is never the picture's neatness: every principal ray must obey its own rule, and the audit checks them one ray at a time.

To evaluate a diagram, take each drawn principal ray in turn and ask: does this ray do what its rule says?

The parallel ray's rule: through a convex lens, it exits through the far focal point; through a concave lens, directly away from the near-side virtual focal point; off a concave mirror, its reflection passes through the focal point.

principal axisobjectimage
The classmate's diagram: tidy, believable, and one ray is breaking its rule.

The center ray's rule, for any thin lens: through the exact center, straight through, no direction change.

The convex lens's third rule: in through the near focal point, out parallel.

A ray that breaks its rule is the flaw. Name the ray, then name the rule it violates.

Thora's classmate drew the center ray bending at the lens. The center ray's rule says straight through: that ray is the flaw.

One broken ray poisons the ending: the false kink moves the crossing, so the image's place, size, or orientation reads wrong.

principal axisobjectimagethe flawed reading
Corrected: the straight center ray moves the crossing, and the image reads differently.

The same audit works on mirror diagrams: check each reflected ray against its own mirror rule.

principal axisfocal pointobjectimage
A mirror diagram under the same audit: check each reflected ray against its own rule.

Neatness proves nothing; the rules decide.

In a convex-lens diagram, the ray through the exact center is drawn bending downward at the lens, and the parallel ray exits through the far focal dot. Evaluate the diagram.

Audit ray by ray. The parallel ray exits through the far focal dot: rule 1 satisfied.

The center ray is drawn bending at the lens. Its rule says: through the exact center, straight through, no direction change.

So the center ray is the wrongly drawn ray, and the rule it violates is the center-ray rule.

The flaw is the center ray: it must continue straight, and this one bends.

In a concave-mirror diagram, the ray that arrived parallel to the principal axis is drawn reflecting straight back parallel, missing the focal dot. Evaluate the diagram.

Audit ray by ray. The parallel ray's mirror rule: its reflection passes through the focal point.

This reflection runs back parallel and never meets the focal dot.

So the parallel ray is the wrongly drawn ray, and the rule it violates is the parallel-ray rule.

The flaw is the parallel ray: its reflection must pass through the focal point, and this one misses it.

In a convex-lens diagram, the ray drawn from the tip arrives parallel and continues through the lens with no bend at all, still parallel. Which drawn ray is wrong?

In a concave-mirror diagram, the ray drawn arriving parallel to the principal axis reflects off the mirror and crosses the principal axis far beyond the focal dot. Which rule does the drawing break?

Stellan says: 'One wrongly drawn ray is enough to put the image in the wrong place.' Is Stellan correct?

Your turn

In Quill's convex-lens diagram, the ray drawn through the exact center of the lens exits at a new angle. Which drawn ray is wrong?

Romilly's diagram draws the center ray of a thin lens bending at the lens plane. Which rule does the drawing break?

In a convex-lens diagram, the ray drawn passing through the near focal point exits the lens still slanting upward, not level. Which rule does the drawing break?