Concave Mirror: Complete Guide, Working, 6 Image Cases & Uses

A concave mirror is a spherical mirror with a reflecting surface that curves inward, like the inside of a bowl or a cave. When parallel light rays strike it, the mirror reflects them inward so they converge at a single point in front of the mirror. This is why it is called a converging mirror. Concave mirrors are the key optical component in reflecting telescopes, car headlights, shaving mirrors, dental mirrors, and solar furnaces. Here is how they work, how to draw their ray diagrams, the six image formation cases, the mirror formula, and where you see them every day.

Picture a cave opening: the walls curve inward, and anything you shout into the cave echoes back toward the centre. A concave mirror does the same thing with light. Its inward-curved surface catches parallel rays and redirects them to meet at a point. The more curved the mirror, the closer that meeting point sits to the surface.

What is a concave mirror? Definition

A concave mirror is a type of spherical mirror where the reflecting surface is the inner (concave) side of a spherical shell. Imagine slicing a hollow sphere and taking the inside surface as your mirror — that is a concave mirror. The outer surface is not used for reflection.

Because the reflecting surface bulges away from the incoming light, rays that hit different points on the mirror are reflected at different angles. The normals at each point point toward the centre of the original sphere, so the reflected rays all head inward. The result is convergence: parallel rays come together at a single spot called the focus.

The essential anatomy: the mirror is a curved line with its reflecting side facing left. The pole (P) is at the centre of the mirror surface. The centre of curvature (C) is the centre of the imaginary sphere the mirror was cut from. The principal focus (F) sits halfway between P and C. Light rays that arrive parallel to the principal axis reflect through F.

Key terms of a concave mirror

Every concave mirror is defined by the same set of reference points. You need these before you can draw ray diagrams or calculate image positions.

• Pole (P): The geometric centre of the mirror's reflecting surface. It lies on the mirror itself.
• Centre of curvature (C): The centre of the imaginary sphere from which the mirror is cut. It lies in front of the mirror, on the principal axis.
• Radius of curvature (R): The distance from the pole to the centre of curvature. This is simply the radius of the original sphere.
• Principal axis: The straight line passing through the pole and the centre of curvature. It is the mirror's axis of symmetry.
• Principal focus (F): The point on the principal axis where parallel rays converge after reflection. For a concave mirror, F lies in front of the mirror, halfway between P and C.
• Focal length (f): The distance from the pole to the principal focus. For a concave mirror, f = R/2.

The relationship between focal length and radius of curvature is one of the simplest in optics: f = R/2. If you know the radius of the mirror's curvature, you immediately know where parallel rays will focus. A mirror with R = 20 cm has a focal length of 10 cm. This is derived from the geometry of paraxial rays — those that strike near the pole at small angles.

How does a concave mirror work?

A concave mirror works by the law of reflection — the same law that governs every mirror. The angle of incidence equals the angle of reflection. What makes a concave mirror special is that the surface normal changes direction at every point along the curve.

At the pole, the normal points straight along the principal axis toward C. Near the edges, the normal tilts inward toward the axis. When parallel rays hit different parts of the mirror, each ray reflects according to the local normal. The result is that all rays are redirected toward the same spot — the focus.

Think of it like a crowd of people standing in a curved line and all throwing a ball to the same person in front. The people at the edges have to throw more toward the centre line, and the people in the middle throw almost straight forward. The curved arrangement makes the convergence happen automatically.

The focusing power depends on the curvature. A deep bowl (short radius) has a short focal length and bends light sharply. A shallow curve (long radius) has a long focal length and bends light gently. This is exactly why a satellite dish uses a concave shape: it concentrates incoming radio waves onto the receiver at the focus.

Concave mirror ray diagram rules

To find where an image forms, you draw at least two rays from a point on the object and see where they meet after reflection. For a concave mirror, you use any two of these four standard rays:

1. Parallel ray: A ray parallel to the principal axis reflects through the principal focus F.
2. Focus ray: A ray passing through the principal focus F reflects parallel to the principal axis.
3. Centre ray: A ray passing through the centre of curvature C hits the mirror along the normal and reflects back along the same path.
4. Pole ray: A ray striking the pole P at an angle reflects at the same angle on the other side of the principal axis.

The image forms where the reflected rays intersect (for a real image) or where they appear to diverge from when traced backward (for a virtual image). The image characteristics — real or virtual, upright or inverted, magnified or diminished — depend entirely on where the object sits relative to F and C.

The Physics Classroom ray diagrams tutorial provides detailed step-by-step guidance for drawing these diagrams along with interactive practice.

Image formation by a concave mirror

There are six standard object positions for a concave mirror, each producing a different image. Here is how the image changes as the object moves from far away to close up:

Object at infinity. When the object is extremely far away (like a star), the rays arrive parallel. They converge at F after reflection. The image is a point-sized, real, inverted image at the focus. This is how a reflecting telescope captures starlight.

Object beyond C. The object is farther than the centre of curvature. The image forms between C and F. It is real, inverted, and diminished (smaller than the object). This is the configuration when a distant landscape is reflected in a concave mirror.

Object at C. The object sits exactly at the centre of curvature. The image forms at C as well. It is real, inverted, and the same size as the object.

Object between C and F. The object is between the centre of curvature and the focus. The image forms beyond C. It is real, inverted, and magnified (larger than the object). This is how a projector works — the film or slide sits between C and F, and a magnified image appears on the screen.

Object at F. The object sits exactly at the focus. The reflected rays are parallel and never meet. The image forms at infinity — it is highly enlarged, real, and inverted. In practice, this is how a spotlight produces a parallel beam: the bulb sits at the focus, and the reflected rays leave parallel.

Object between F and P. The object is between the focus and the pole. The reflected rays diverge, so you trace them backward to find their meeting point behind the mirror. The image is virtual, upright, and magnified. This is how a shaving mirror works — you hold your face within the focal length to see an enlarged upright reflection.

Mirror formula and magnification

The mirror formula relates the object distance (u), image distance (v), and focal length (f):

1/f = 1/u + 1/v

By the Cartesian sign convention for concave mirrors:

• u is always negative (object in front of the mirror)
• f is negative (focus in front of the mirror)
• v is negative for real images (in front) and positive for virtual images (behind)

Magnification (m) = -v/u = height of image / height of object

A negative magnification means the image is inverted (real). A positive magnification means the image is upright (virtual). If |m| > 1, the image is magnified; if |m| < 1, it is diminished.

Worked example: An object is placed 15 cm in front of a concave mirror with a focal length of 10 cm. Where does the image form?

Using f = -10 cm, u = -15 cm: 1/v = 1/f - 1/u = 1/(-10) - 1/(-15) = -1/10 + 1/15 = -3/30 + 2/30 = -1/30 So v = -30 cm.

The negative v means the image is 30 cm in front of the mirror — real. Magnification m = -v/u = -(-30)/(-15) = -2. The image is twice the object size and inverted.

Uses of concave mirrors

Concave mirrors appear in more everyday devices than you might expect. Here are the most important applications:

Reflecting telescopes. A large concave mirror (the primary mirror) gathers light from distant stars and brings it to a focus. The larger the mirror, the more light it collects and the fainter the objects you can see. The Hubble Space Telescope uses a 2.4-metre concave primary mirror. The BYJU's guide to concave mirror image formation provides additional worked examples and detailed sign convention explanations.

Vehicle headlights and torches. The bulb sits at the focus of a concave reflector. Light that travels backward from the bulb hits the mirror and reflects forward as a parallel beam. This is why a torch beam stays narrow over distance — the concave mirror collimates the light.

Shaving mirrors. A concave mirror with the user's face inside the focal length produces a magnified, upright, virtual image. This makes it easier to see small details while shaving or applying makeup.

Dental mirrors. Dentists use small concave mirrors to see magnified, upright images of teeth. The mirror is held close enough that the tooth sits between the focus and the mirror surface.

Solar furnaces. Large arrays of concave mirrors concentrate sunlight onto a small area, producing intense heat. The world's largest solar furnace in Odeillo, France, uses thousands of concave mirror facets to reach temperatures over 3,000 °C.

Laser optical cavities. Two concave mirrors facing each other form the resonant cavity of many lasers. The mirrors bounce light back and forth through the gain medium, amplifying it with each pass.

For a side-by-side comparison with the outward-curving type, see the guide on concave vs convex mirror. The broader physics of how light reflects from surfaces is covered in our reflection of light examples guide.

Common misconception: "Concave mirrors always magnify"

It is easy to remember "concave = caves in" and assume this always magnifies, but magnification depends entirely on the object's distance. A concave mirror can produce diminished images (object beyond C), same-size images (object at C), or magnified images (object between C and F or between F and P). The mirror does not have a fixed magnification — it depends on where you put the object.

A related misconception is that "concave mirrors only produce real images." In fact, they produce virtual, upright, magnified images whenever the object sits between the focus and the pole. This is exactly the configuration for shaving mirrors and dental mirrors. The ability to switch between real and virtual images is what makes concave mirrors so versatile.

Concave mirror vs convex mirror at a glance

For a full comparison, see the detailed concave vs convex mirror guide. For understanding how mirrors differ from lenses, read our lens vs mirror comparison.

Summary

A concave mirror is a converging spherical mirror that reflects light inward to a focus. Its key parameters — focal length, radius of curvature, centre of curvature, and pole — define how it forms images. The mirror formula 1/f = 1/u + 1/v and magnification m = -v/u describe its behaviour precisely. Depending on the object's position, a concave mirror can produce real or virtual, inverted or upright, and diminished or magnified images. Concave mirrors are used in telescopes, headlights, torches, shaving mirrors, dental mirrors, solar furnaces, and laser cavities — making them one of the most important curved mirrors in optics. For the opposite type, see our guide on convex mirror.