← Lenses and images

Determine the full image for any mirror or lens

Romilly leans toward her makeup mirror, her chin well inside its focal length, and sees her face enlarged and right-way-up. One question closes this topic: given ANY mirror or lens and ANY object position, what exactly does it show?

Everything needed is already on the bench: the constructions for all seven cases, and the three-question read. The capstone is the full routine, run end to end on any case.

The full routine has four steps, always in this order.

Step 1, place the case: name the element, and compare the object's distance with the focal length. Inside or beyond the focal point is the deciding read.

principal axisfocal pointobjectobject distancefocal length
Step 1, place the case: concave mirror, object inside the focal length.

Step 2, pick the construction that case owns: the mirror rules for a mirror, the lens rules for a lens; two known rays from the object's tip.

Step 3, construct: draw the two rays, find where they meet, or where their dashed trace-backs meet.

Step 4, read the finished drawing with the three questions: kind and location, orientation, size.

Romilly's case, placed: a concave mirror, face INSIDE the focal length.

Constructed: the reflected beam's rays spread, and their dashed trace-backs meet behind the mirror.

principal axisfocal pointobjectobject distancefocal lengthimage
Steps 2 and 3, construct: the trace-backs meet behind the mirror.

Read: virtual, behind the mirror; same side of the principal axis, so upright; the traced arrow taller, so enlarged.

principal axisfocal pointobjectobject distancefocal lengthimage1233
Step 4, read: virtual and behind the mirror, upright, enlarged.

The full answer: her makeup mirror shows a virtual, upright, enlarged face, located behind the mirror.

Any case in this topic yields to the same four steps. No formula is needed: the drawing, built and read, is the whole tool.
Every case, one routinecaserays to drawendingplane mirrortwo reflected rays, traced backvirtual, upright, same size, behindconcave mirror, object beyond the focal pointmirror rulesreal, inverted, in frontconcave mirror, object inside the focal pointmirror rules, traced backvirtual, upright, enlarged, behindconvex mirror, any positionmirror rules, traced backvirtual, upright, reduced, behindconvex lens, object beyond the focal pointlens rules 1 and 2real, inverted, far sideconvex lens, object inside the focal pointlens rules 1 and 2, traced backvirtual, upright, enlarged, object's sideconcave lens, any positionlens rules 1 and 2, traced backvirtual, upright, reduced, object's side
Every case this topic owns, one routine: place it, draw it, read it.

Run the full routine: an ornament stands 20 cm from a convex mirror of focal length 10 cm. Determine the full image description.

Step 1: a convex mirror; its profile does not switch with position, but run the drawing anyway.

Step 2: the mirror toolkit; the parallel ray reflects as if from the virtual focal point behind the mirror, and the center-strike ray reflects at the equal angle.

Step 3: the reflected rays spread; their dashed trace-backs meet behind the mirror.

Step 4: dashed-only meeting behind the mirror, same side as the tip, traced arrow shorter.

Virtual, upright, reduced, located behind the mirror.

Run the full routine: a key sits 7 cm from a convex lens of focal length 15 cm. Determine the full image description.

Step 1: a convex lens, and 7 cm is less than 15 cm, so the key sits inside the focal point.

Step 2: the lens toolkit: the parallel ray and the center ray.

Step 3: the refracted rays spread; their dashed trace-backs meet on the key's side, higher and farther out.

Step 4: dashed-only meeting on the object's side, same side as the tip, traced arrow taller.

Virtual, upright, enlarged, on the key's side of the lens.

The full routine's step 1 places the case. Which comparison does that step make?

A bead sits 3 cm from a convex lens of focal length 8 cm. Run the routine. What is the full image description?

A toy soldier stands 25 cm from a concave lens of focal length 10 cm. Run the routine. What is the full image description?

Your turn

A face leans 8 cm from a concave makeup mirror of focal length 20 cm. Determine the full image description.

A mailbox stands 3 m from a convex mirror of focal length 1 m on a driveway pole. Determine the full image description.

A model house sits 30 cm from a convex lens of focal length 12 cm. Determine the full image description.