Concave and convex mirrors are the two types of spherical mirrors, and they are opposites in every important way. One curves inward like a cave and converges light to a point. The other curves outward like a dome and spreads light apart. These differences lead to completely different image properties and uses. Here is a direct side-by-side comparison of concave vs convex mirrors — covering shape, light behaviour, image formation for every object position, ray diagrams, sign conventions, and real-world applications — plus a simple trick to keep them straight.
The easiest way to tell them apart: concave mirrors make fire, convex mirrors make things smaller. If you hold a concave mirror in sunlight, it focuses the rays to a hot spot that can ignite paper. A convex mirror can never do that — it spreads sunlight out instead.
What is a concave mirror? (Brief recap)
A concave mirror is a spherical mirror where the reflecting surface curves inward — like the inside of a bowl or a cave. It is called a converging mirror because it reflects parallel light rays inward to meet at a single focal point (F) in front of the mirror. The centre of curvature (C) also lies in front. The focal length is negative by the Cartesian sign convention.
Concave mirrors can produce both real and virtual images depending on the object's distance. When the object is beyond the focus, the image is real and inverted. When the object is between the focus and the pole, the image is virtual, upright, and magnified. This versatility makes concave mirrors the choice for telescopes, headlights, shaving mirrors, and solar concentrators.
For full detail, see the complete guide on concave mirrors.
What is a convex mirror? (Brief recap)
A convex mirror is a spherical mirror where the reflecting surface curves outward — like the outside of a dome or a fish-eye lens. It is called a diverging mirror because it reflects parallel light rays outward so they appear to come from a focal point (F) behind the mirror. The centre of curvature (C) also lies behind. The focal length is positive by the Cartesian sign convention.
Convex mirrors always produce virtual, upright, and diminished images regardless of the object's position. This consistent behaviour and the wide field of view make convex mirrors the standard for vehicle side mirrors, security mirrors, and traffic safety mirrors. The trade-off is that objects appear smaller and farther than they really are — hence the warning "objects in mirror are closer than they appear."
For full detail, see the complete guide on convex mirrors.
Key differences between concave and convex mirrors
| Property | Concave Mirror | Convex Mirror |
|---|---|---|
| Shape | Curves inward (like a cave) | Curves outward (like a dome) |
| Light behaviour | Converges (brings rays together) | Diverges (spreads rays apart) |
| Focal point | In front of mirror | Behind mirror |
| Centre of curvature | In front of mirror | Behind mirror |
| Focal length sign | Negative | Positive |
| Image types | Real or virtual | Virtual only |
| Image orientation | Inverted (real) or upright (virtual) | Always upright |
| Image size | Diminished, same, or magnified | Always diminished |
| Field of view | Narrow (focused) | Wide (panoramic) |
| Starting a fire | Yes (concentrates sunlight to a point) | No (spreads sunlight out) |
| Mirror formula | 1/f = 1/u + 1/v (with f negative) | 1/f = 1/u + 1/v (with f positive) |
The single most important difference: a concave mirror can form a real image that you can project onto a screen. A convex mirror can only form a virtual image behind the mirror that cannot be projected. This difference follows directly from convergence vs divergence.
Image formation: concave mirror vs convex mirror
The table below shows what happens for every possible object position. Notice that the concave mirror has six distinct cases with different outcomes, while the convex mirror has only two cases with the same outcome every time.
| Object Position | Concave Mirror Image | Convex Mirror Image |
|---|---|---|
| At infinity | At F; point-sized, real, inverted | At F behind mirror; point-sized, virtual, upright |
| Beyond C | Between C and F; diminished, real, inverted | Between P and F behind mirror; diminished, virtual, upright |
| At C | At C; same size, real, inverted | Between P and F behind mirror; diminished, virtual, upright |
| Between C and F | Beyond C; magnified, real, inverted | Between P and F behind mirror; diminished, virtual, upright |
| At F | At infinity; highly magnified, real, inverted | Between P and F behind mirror; diminished, virtual, upright |
| Between F and P | Behind mirror; magnified, virtual, upright | Between P and F behind mirror; diminished, virtual, upright |
The convex mirror column is repetitive by design — it always produces the same type of image. This simplicity is why convex mirrors are so predictable and reliable for safety applications where you need to know exactly what you will see.
Concave mirror ray diagram rules
- Parallel ray: A ray parallel to the principal axis reflects through F in front.
- Focus ray: A ray through F reflects parallel to the principal axis.
- Centre ray: A ray through C hits the mirror along the normal and reflects back on itself.
- Pole ray: A ray striking the pole reflects symmetrically about the principal axis.
Convex mirror ray diagram rules
- Parallel ray: A ray parallel to the principal axis reflects so its extension passes through F behind the mirror.
- Focus ray: A ray directed toward F behind the mirror reflects parallel to the principal axis.
- Centre ray: A ray directed toward C behind the mirror reflects back along the same path.
The key difference: concave mirror rays actually meet in front (real intersection), while convex mirror rays only appear to meet when traced backward (virtual intersection).
How to remember concave vs convex
Here are three memory tricks that work:
1. "Concave has 'cave'" — The word "concave" contains "cave." A cave curves inward. Draw a cave opening: the walls curve in. That is exactly how a concave mirror looks from the reflecting side.
2. "Convex makes things smaller" — Stand in front of a convex mirror and you look smaller. Stand in front of a concave mirror (within the focal length, like a shaving mirror) and you look bigger. If the image is smaller, it is convex. If it could ever be larger, check for concave.
3. The fire test — A concave mirror can focus sunlight to start a fire. A convex mirror cannot. If you see someone using a curved mirror to ignite something, it is concave — the converging type. A convex mirror would spread the sunlight harmlessly.
Mirror formula comparison
Both mirrors use the same mirror formula:
1/f = 1/u + 1/v
| Quantity | Concave Mirror | Convex Mirror |
|---|---|---|
| Focal length (f) | Negative | Positive |
| Object distance (u) | Negative | Negative |
| Image distance (v) | Negative (real) or positive (virtual) | Positive (always virtual) |
| Magnification (m) | Negative (inverted) or positive (upright) | Positive and less than 1 |
The sign convention difference for f is the most important thing to remember when solving problems. For a concave mirror, f is negative. For a convex mirror, f is positive.
Applications side by side
| Application | Mirror Type | Why That Type |
|---|---|---|
| Reflecting telescope primary | Concave | Needs to collect and focus distant starlight to a point |
| Vehicle headlight | Concave | Bulb at focus produces a parallel beam |
| Shaving / makeup mirror | Concave | Magnified upright image when face is within focal length |
| Dental mirror | Concave | Magnified upright view of individual teeth |
| Solar furnace | Concave | Concentrates sunlight onto a small area for high heat |
| Laser cavity | Concave | Two concave mirrors bounce light back and forth to amplify it |
| Car side-view mirror | Convex | Wide field of view to see adjacent lanes |
| Security / surveillance mirror | Convex | Single mirror covers an entire aisle or room |
| Traffic safety mirror (blind corner) | Convex | Lets drivers see around a corner without creeping forward |
| ATM security mirror | Convex | User can see the area behind them while at the machine |
| Street light reflector | Convex | Spreads light over a wide area rather than focusing it |
The pattern is clear: if you need to concentrate or focus light, use a concave mirror. If you need to spread or widen the view, use a convex mirror.
Common misconceptions about concave and convex mirrors
"Concave mirrors always magnify." No — a concave mirror only magnifies when the object is between the focus and the pole (virtual image) or between C and F (real image). When the object is beyond C, the image is actually diminished. The magnification depends on the object's position.
"Convex mirrors produce real images because I can see them." What you see when you look at a convex mirror is a virtual image formed behind the mirror. Your eye lens then focuses that virtual image onto your retina, but the mirror itself never produces a real, projectable image. The reflected rays from a convex mirror always diverge.
"The 'objects are closer than they appear' warning means the mirror is faulty." It is not a flaw — it is a deliberate trade-off. The convex curve gives a wider field of view (more safety) at the cost of accurate distance perception. The warning exists so drivers learn to compensate.
"Concave and convex mirrors follow different formulas." They use the exact same mirror formula (1/f = 1/u + 1/v) and magnification formula (m = -v/u). The only difference is the signs of f and v, which follow directly from the mirror's shape.
"A convex mirror can produce a magnified image if the object is very close." Even when the object touches the pole of a convex mirror, the image remains diminished. The limit is an image the same size as the object when the object is at the pole — but the image is never magnified. This is fundamentally different from a concave mirror, which produces a magnified image when the object is within the focal length.
Summary
Concave and convex mirrors are opposites in shape and behaviour. A concave mirror curves inward like a cave, converges light, has a negative focal length, and can produce both real and virtual images of varying sizes. A convex mirror curves outward like a dome, diverges light, has a positive focal length, and always produces a virtual, upright, diminished image.
Choose a concave mirror when you need to focus light — telescopes, headlights, shaving mirrors, solar furnaces. Choose a convex mirror when you need a wide field of view — car mirrors, security mirrors, traffic safety mirrors. The mirror formula and ray diagram rules are the same for both; only the signs and the convergence/divergence behaviour differ.
For more detail on each type, see the standalone guides on concave mirrors and convex mirrors. For how curved mirrors compare to lenses, read our lens vs mirror comparison guide.
Frequently Asked Questions
What is the difference between a concave and convex mirror?
A concave mirror curves inward (like a cave) and converges parallel light rays to a focal point in front of the mirror. A convex mirror curves outward (like a dome) and diverges parallel rays so they appear to come from a focal point behind the mirror. Concave mirrors can form real or virtual images; convex mirrors only form virtual images. Concave mirrors are used for focusing light in telescopes and headlights; convex mirrors are used for wide-angle viewing in rearview and security mirrors.
How can I remember concave vs convex?
Think of the word 'concave' — it contains 'cave'. A cave curves inward. The word 'convex' looks like 'vex' — a vexing, bulging shape that curves outward. A memory trick: concave mirrors start fires (converge sunlight to a point); convex mirrors spread light (they diverge it). Another trick: 'con-cave' means 'with cave' — the surface caves in.
Which mirror has a wider field of view — concave or convex?
Convex mirrors provide a much wider field of view than concave or plane mirrors because the outward curve reflects light from a larger area into the viewer's eye. This is why convex mirrors are used as side-view mirrors in cars and security mirrors in shops. The trade-off is that objects appear smaller and farther than they actually are.
Can a convex mirror produce a real image?
No. A convex mirror always diverges reflected rays, so the rays never converge in front of the mirror. The image is always virtual, upright, and diminished, regardless of the object's position. Only concave mirrors can produce real images, and only when the object is placed beyond the focal point.
What is the focal length sign for concave and convex mirrors?
By the Cartesian sign convention, the focal length of a concave mirror is negative (focus is in front of the mirror), and the focal length of a convex mirror is positive (focus is behind the mirror). The focal length of both is calculated by f = R/2, where R is the radius of curvature.
Which mirror is used in vehicle headlights — concave or convex?
Vehicle headlights use a concave mirror (reflector) behind the bulb. The bulb is placed at the focus of the concave reflector, so light that travels backward from the bulb is reflected forward as a parallel beam. This gives the headlight its narrow, long-range beam. A convex mirror would spread the light too widely.
Why do convex mirrors say 'objects are closer than they appear'?
Convex mirrors produce a diminished (smaller) image, which makes objects look farther away than they actually are. The warning reminds drivers that a vehicle seen in the passenger-side mirror is closer than the image suggests, so they should check before changing lanes. The mirror trades accurate distance perception for a wider field of view.
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