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Convex Mirror Simulator: Divergence and Virtual Focus

A convex mirror spreads a parallel beam. Follow the real reflected rays and their dashed backward extensions to understand its virtual focus.

Try the mirror experiment

Free, live optical simulation. Change one setting and observe the result.

The controls and explanation below describe this experiment. A browser with Canvas support is required to draw the rays.

Preparing the optical trace…

Open this setup in Free lab →

Exact reflection from a spherical arc. Perfect front reflectivity and an absorbing back are idealized; F is a paraxial reference.

What is a convex mirror?

A convex mirror reflects from the outward-curving side of its surface. Rays arriving parallel to the optical axis return in diverging directions. Their backward extensions appear to come from a point behind the mirror. That point is a virtual focus: it is not a place where transmitted light has actually collected.

The component here is an ideal spherical reflector. The silver curve is its reflecting front; the opposite side absorbs light. The simulator finds the actual circular intersection and local normal for every ray, so it can show the effect of changing curvature rather than replaying a fixed animation.

Read the convex mirror ray diagram

  1. Identify the incoming parallel beam and the rays returning from the convex face.
  2. Keep Optics guides enabled to see dashed backward extensions behind the mirror.
  3. Compare those extensions with F≈, the near-axis virtual-focus estimate.
  4. Increase R to make the surface flatter, or reduce it to increase curvature.
  5. Change beam width to compare near-axis rays with rays closer to the edges.

The dashed lines are drawing aids and carry no simulated energy. A detector behind the mirror will not receive power just because a dashed extension passes through it. Use Fit view if you zoom in too far, and open the setup in Free lab to experiment with placement and rotation.

Why is the focal length negative?

Using the real-is-positive mirror convention, a convex mirror has f ≈ −R/2. The negative sign places the virtual focus behind the reflecting vertex. At the default R = 360 model units, the paraxial focal length is approximately −180 units.

A sphere is not an ideal point-focusing surface for every ray. The backward extensions of a wide beam do not all cross at exactly one point. The F≈ marker intentionally remains a reference rather than forcing the traced rays to pass through it. Reference: OpenStax on spherical mirrors and sign conventions.

Convex mirror images: upright, virtual and reduced

For a real object in front of a convex mirror, the usual paraxial model predicts a virtual, upright and reduced image. The mirror equation is 1/f = 1/do + 1/di. Magnification is m = −di/do; a positive value indicates an upright image.

As a worked example, let f = −180 and do = 540 in matching units. Then di = −135 and m = +0.25. The estimated image is behind the mirror and one quarter the object height. The live scene above demonstrates beam divergence and virtual extensions, not a rendered image of an extended object.

Concave mirror vs convex mirror

PropertyConcave spherical mirrorConvex spherical mirror
Reflecting faceCurves inwardCurves outward
Near-axis parallel beamConverges in frontDiverges after reflection
Paraxial focal signPositiveNegative
Typical puzzle roleGather returning lightSpread or reshape returning light

Try the same beam width and radius in the concave mirror simulator. Compare the direction of actual light, the focus reference and the space needed around the reflector. A larger radius makes either spherical surface locally more like a plane mirror.

Building a wider light route

A convex mirror can spread a narrow beam across a wider region, but spreading does not multiply its power. A small receiver may intercept a smaller share of the original beam as the light spreads. Two receivers can also compete for it because an absorbing receiver stops the rays it catches.

In Free lab, combine the curved reflector with a lens, aperture or splitter to explore those tradeoffs. The mirror's orientation matters: turning the hatched back toward the source causes absorption, not a second concave reflecting surface. This prevents the component from silently changing its physical identity when flipped.

Model boundaries

This is a two-dimensional geometric-optics scene with ideal front reflectivity. It does not reproduce coating losses, surface imperfections, coating-specific polarization effects, diffraction or a complete three-dimensional field of view. Wavelength changes affect the displayed band, but the ideal reflecting geometry is achromatic.

You can inspect absorbed wavelength power in the spectral detector experiment. The free simulators and explanations are available without payment; the existing Prism Riddle campaign still has three free chambers and 80 chambers in total.

Frequently asked questions

Why does a convex mirror have a virtual focus?

The real reflected rays diverge. Their backward extensions approximately meet behind the mirror; no light needs to travel there.

Is light transmitted through the mirror to the dashed lines?

No. The dashed lines are virtual drawing aids. The front reflects and the back absorbs in this model.

What happens when I increase the radius?

The spherical surface becomes flatter. Its near-axis focal distance has a greater magnitude.

What image does a convex mirror form?

For a real object in front of it, the paraxial model predicts a virtual, upright and reduced image. The interactive scene itself traces a beam rather than an extended object.

Can I switch between concave and convex mirrors?

Yes. Both types are separate tools and presets in Free lab; the linked concave mirror page provides a matching interactive comparison.

Play the first three chambers free →