What is a concave mirror?
A concave mirror reflects from the inward-curving side of its surface. A narrow bundle of rays parallel to its optical axis returns toward a focus in front of the mirror. This makes a curved reflector useful when a light path must both turn back and become narrower.
In this simulator, the mirror is a section of a sphere viewed in two dimensions. Each ray meets the circular surface at its own point, and its reflection is calculated from the local surface normal. The ray diagram is not drawn toward a predetermined answer.
How to use the concave mirror simulator
- Start with the white parallel beam and note the near-axis focus marker, F≈.
- Reduce the beam width. The returning rays gather close to that reference point.
- Increase the width to include rays farther from the axis. Their crossing positions spread out.
- Change the radius of curvature, R. A larger radius gives a flatter mirror and a more distant near-axis focus.
- Use Optics guides to compare the axis, the center of curvature C, and the computed light. Fit view restores the whole scene after zooming.
The source-color control changes the sampled band emitted by the lamp. Our ideal mirror uses the same geometry for every wavelength, so changing red to blue does not change its reflection angle. Open the setup in Free lab to move the source, rotate the mirror or combine it with lenses and filters.
Concave mirror focal length: when does f = R/2 apply?
For rays close to the optical axis, a spherical mirror has an approximate focal length of f ≈ R/2. With R = 360 model units, the near-axis reference is 180 units in front of the vertex. These are consistent simulation distances, not a claim that the canvas is calibrated in centimeters.
The approximation has a limit. Wider beams strike more strongly tilted parts of the sphere, and those marginal rays cross the axis at different distances. The visible spread is spherical aberration. A parabolic mirror has a different shape and can focus an axis-parallel beam without this particular spherical error; the component here is explicitly spherical. Reference: OpenStax on spherical mirrors.
Concave mirror images and the mirror equation
A ray diagram of a beam is different from an image of an extended object. The interactive experiment above follows a parallel beam; it does not render a photograph or an arrow-shaped object. For an object near the optical axis, the mirror equation provides a separate useful estimate: 1/f = 1/do + 1/di, with magnification m = −di/do.
For example, take f = 180 and an object distance of 540 in the same units. The estimated image distance is 270, and m = −0.5: a real, inverted image half the object's height. An object inside the focal distance instead produces a virtual, upright image. Do not confuse the F marker for a parallel beam with the image position of every possible object.
Using a concave mirror in a light puzzle
A returning beam introduces a different planning problem from a transmitting lens. A detector placed on the incoming path may absorb the light before it reaches the mirror. Move it away from that path, or design a splitter arrangement that separates the incoming and returning branches. In Free lab you can test that geometry directly.
If a wide reflected beam misses a small receiver, first inspect its crossing region. Narrowing the incident beam can reduce spherical aberration, but an aperture also removes energy. This creates a useful tradeoff between concentrating the light and preserving enough power for a target.
What this experiment does and does not model
The curved surface is intersected analytically. Reflection on its silver front is ideal and lossless; its hatched back absorbs light. Surface roughness, coating-dependent reflectivity and polarization response, diffraction and out-of-plane effects are not included. The camera zoom changes your view, not the optical geometry.
Compare the convex mirror simulator for outward reflection, or use the spectral detector experiment to inspect received wavelength power. These free experiments supplement Prism Riddle's existing 80 puzzle chambers; they do not unlock paid chambers or reveal their solutions.