Concave Ray Diagram Mirror: How to Draw Every Image Case Step by Step

Short answer

• A concave ray diagram mirror drawing starts with a mirror curving inward like the inside of a bowl. Mark the vertex at the mirror surface center, the center of curvature, labeled C, and the focal point, labeled F, on a horizontal line called the principal axis. F sits halfway between vertex and C, so focal length is one half of radius of curvature. From the top of an upright object, draw two or more principal rays, follow each reflected ray, and mark the image where reflected rays meet, or where backward extensions meet. When the object is farther than F, the image is real and inverted. When closer than F, it is virtual, upright, and larger. The five cases below give size and location for every standard position.

What a Concave Mirror Is

A concave mirror is a spherical mirror whose reflecting surface is on the inside of the sphere: a small piece cut from a hollow ball, shiny side facing inward. That inward curve separates it from a convex mirror, whose surface bulges outward. This article covers concave mirrors only. A convex mirror is separate, noted at the end only as an internal link candidate, because its rules differ.

The word concave is often linked to the word cave, because the surface curves inward like a cave entrance. That aid helps with the definition, but not with the image. The image depends on geometry: object position, center of curvature, and focal point. A ray diagram turns that geometry into a picture checked ray by ray. Concave mirrors are also called converging mirrors, because rays arriving parallel to the principal axis reflect toward a region near the focal point. In an ideal diagram they meet there; in a real spherical mirror that holds only under the approximation below.

The Parts of the Diagram You Must Label

A clear diagram needs the same labels every time. Without them, the reader cannot tell whether an image is between F and C, or beyond C, and that distinction changes the answer. Draw a short curved arc, concave side facing the object. In most diagrams the object stands on the left and the mirror curves to the right. The center of the mirror surface is the vertex, labeled V. Some textbooks use P for pole for the same point, but this guide uses V.

Draw a horizontal dashed line through the vertex. That line is the principal axis, sometimes called the optical axis, running through vertex, focal point, and center of curvature. Every ray rule is stated in relation to it, so draw it first. The center of curvature, labeled C, is the center of the sphere from which the mirror segment was cut. The distance from vertex to C is the radius of curvature, labeled R. The focal point, labeled F, lies between vertex and C. The distance from vertex to F is the focal length, labeled f. In the small angle approximation, also called the paraxial approximation, f equals R divided by 2. So C is twice as far from the mirror as F.

The object is usually an upright arrow on the principal axis, base on the axis and tip above it. Trace the tip: once you know where the image tip falls, drop a line to the axis to find the image base. If the image tip falls below the axis while the object tip is above it, the image is inverted; if above, it is upright. Four descriptors should always be stated together. Real means reflected rays actually meet in front of the mirror, so the image can be projected onto a screen. Virtual means only backward extensions meet behind the mirror, so it cannot be projected but can be seen in the mirror. Inverted and upright describe direction, larger, smaller, and same size describe height, and location states where the image sits relative to mirror, F, and C, or behind the mirror.

The Small Angle Approximation

A spherical mirror diagram uses an approximation. Rays staying close to the principal axis and making only a small angle with it are called paraxial rays. For those rays, a spherical mirror behaves much like a parabolic mirror, and parallel rays reflect through a well defined focal point. Rays striking far from the axis do not all pass through exactly the same point. That spread is called spherical aberration, and it can blur an extended image. A textbook diagram is therefore not a claim that every ray meets at one perfect point. It is a model that works well for paraxial rays and predicts type, orientation, size, and location in the standard cases.

How to Read a Ray Diagram

A diagram has three kinds of lines. Solid lines show real paths in front of the mirror. Dashed lines behind the mirror show backward extensions, used only for a virtual image. The principal axis is also dashed in many diagrams, but it is a reference line, not a light ray. Start at the object tip. Follow one principal ray to the mirror, then its reflected path, then do the same for a second ray. Where reflected paths cross in front, that point is the tip of a real image. Where they do not cross in front, extend both backward with dashed lines behind the mirror; where those extensions cross is the tip of a virtual image. Two rays locate an image point. A third ray is a check: if it misses that point, something is wrong.

The Three Principal Rays in Words

The three principal rays are the parallel ray, the focal ray, and the center ray. Each starts at the object tip, with a simple incoming and reflected path. Learn them as pairs, incoming plus reflected.

Ray 1 is the parallel ray. It leaves the object tip parallel to the principal axis. After reflection, it passes through F. In words: parallel in, through F out. It is often easiest first, because a line parallel to the axis is easy to keep straight. Ray 2 is the focal ray. It leaves the object tip along a line through F, then strikes the mirror. After reflection, it travels parallel to the axis. In words: through F in, parallel out. Ray 1 and Ray 2 are reverse partners, and that pairing helps prevent swapping them. Ray 3 is the center ray. It leaves the object tip along a line through C, then strikes the mirror. Because that line meets the surface at a right angle, along the normal, the ray reflects back along the same line. In words: through C in, back along the same line out. Any bend here is easy to spot, because incoming and reflected segments must lie on one straight line through C.

OpenStax lists four principal rays, adding a vertex ray striking the vertex and reflecting symmetrically about the axis. This guide uses the three rays above, enough for every case here. The vertex ray remains a valid extra check. To draw any ray, place a ruler from the object tip along the incoming direction, mark where it meets the mirror, then draw the reflected segment.

A Step by Step Method for Every Case

Use the same steps for each position; only the result changes. First, draw mirror arc, principal axis, and V, F, and C in that order outward, with F halfway between V and C. Second, draw the object arrow, base on the axis. Third, draw Ray 1 parallel to the axis, then through F. Fourth, draw Ray 2 through F, then parallel to the axis. Fifth, draw Ray 3 through C, then back along the same line. Sixth, mark the image tip where reflected rays meet, or where dashed extensions meet behind the mirror. Seventh, draw the image arrow and state type, orientation, size, and location. If reflected rays are parallel, the image is at infinity, the case for an object at F. If they spread apart, extend them backward.

Case 1: Object Beyond the Center of Curvature

Place the object farther from the mirror than C, so the object distance is greater than 2f, because C sits at 2f. Draw Ray 1 parallel to the axis, then through F after reflection. Draw Ray 2 through F, then parallel to the axis after reflection. Those reflected rays cross between F and C. Draw Ray 3 through C, then back along the same line. It passes through the same crossing point, confirming the result. The image tip falls below the axis, so drop a line to the axis to complete the image arrow. The image is real, because reflected rays actually meet in front of the mirror. It is inverted, pointing downward while the object points upward. It is smaller, also described as diminished. Its location is between F and C, in front of the mirror. In short form: object beyond C gives a real, inverted, smaller image between F and C. As the object moves farther away, the image moves closer to F and becomes smaller still. In the limit, a very distant object sends effectively parallel rays, and the image forms very close to F as a tiny inverted point, sometimes listed as object at infinity, image at F, real, inverted, and highly diminished.

Case 2: Object at the Center of Curvature

Place the object exactly at C, so the object distance equals 2f. Draw Ray 1 parallel to the axis, then through F after reflection. Draw Ray 2 through F, then parallel to the axis after reflection. Those reflected rays cross exactly at C, at the image tip height. Draw Ray 3 through C, then back along the same line. It passes through the same image point at C. The image tip falls below the axis at the same height, in absolute terms, as the object tip is above it, so the image arrow has the same length as the object arrow. The image is real, because rays meet in front of the mirror. It is inverted, pointing downward. It is the same size as the object. Its location is at C. In short form: object at C gives a real, inverted, same size image at C. If a diagram here gives a different location or size, check that F is truly halfway between V and C.

Case 3: Object Between the Center of Curvature and the Focal Point

Place the object between C and F, so the object distance is greater than f but less than 2f. This is where a concave mirror starts to magnify a real image. Draw Ray 1 parallel to the axis, then through F after reflection. Draw Ray 2 through F, then parallel to the axis after reflection. This time the reflected rays cross beyond C, farther from the mirror than C itself. Draw Ray 3 through C, then back along the same line. It passes through the same crossing point beyond C. The image tip falls below the axis, farther from it than the object tip is above it, so the image arrow is longer than the object arrow. The image is real, because rays meet in front of the mirror. It is inverted, pointing downward. It is larger, also described as magnified or enlarged. Its location is beyond C, in front of the mirror. In short form: object between C and F gives a real, inverted, larger image beyond C. As the object moves inward from beyond C, through C, and toward F, the real inverted image moves outward and grows larger.

Case 4: Object at the Focal Point

Place the object exactly at F, so object distance equals f. This is the boundary between real and virtual images, and its diagram looks different. Draw Ray 1 parallel to the axis, then through F: it leaves the tip horizontally, strikes the mirror, then heads diagonally down through F. The focal ray is degenerate exactly at F: a ray from the tip through F does not strike the mirror, so Case 4 is drawn from Ray 1 and Ray 3, whose reflected lines are parallel. The two reflected rays are now parallel, and parallel lines do not meet at a finite point. Ray 3 through C, back along the same line, gives no single finite crossing point with them in the ideal diagram.

The standard description is that the image is formed at infinity, described as real, inverted, and highly enlarged, because rays would meet only at an unbounded distance. In reverse, a source at F gives reflected rays leaving as a near parallel beam, the principle for torches, searchlights, and headlight reflectors, with the parabolic qualification in the uses section. Do not force a finite image point here. If reflected rays cross neatly for an object exactly at F, the object was not exactly at F, or a ray was drawn wrongly.

Case 5: Object Inside the Focal Point

Place the object between F and the mirror, so object distance is less than f. This is the magnifying mirror case most people meet first in daily life. Draw Ray 1 parallel to the axis, then through F. After reflection it heads away from the axis, downward and outward. Draw Ray 2 along a line through F, then parallel to the axis. Note the direction: the line from the object tip backward passes through F, while the forward segment goes to the mirror and then leaves parallel to the axis. Draw Ray 3 through C, then back along the same line. After reflection it also heads away from the axis. None of these reflected rays meet in front of the mirror.

Extend each reflected ray backward behind the mirror with dashed lines. Those extensions meet behind the mirror, above the axis, farther from the mirror and higher above the axis than the object tip. Draw the image arrow from the axis behind the mirror up to that point, using dashed lines in many textbook styles, to show it is not formed by real rays meeting there. The image is virtual, because only backward extensions meet, behind the mirror. It is upright, pointing upward like the object. It is larger, also described as magnified or enlarged. Its location is behind the mirror. In short form: object inside F gives a virtual, upright, larger image behind the mirror. This is the only standard case with an upright or virtual image.

Summary of All Five Cases

From far to near, the object moves inward, the image moves outward, then type flips at F. Object beyond C: real, inverted, smaller, between F and C. Object at C: real, inverted, same size, at C. Object between C and F: real, inverted, larger, beyond C. Object at F: image at infinity, real, inverted, highly enlarged, reflected rays parallel. Object inside F: virtual, upright, larger, behind the mirror. Every diagram should end with all four descriptors: type, orientation, size, and location. Leaving out location is the most common incomplete answer, because Case 1 and Case 3 are both real and inverted but differ in size and location.

Checking a Diagram With the Mirror Equation

A ray diagram gives a visual answer; the mirror equation gives a numerical check. In the small angle approximation, 1 divided by object distance plus 1 divided by image distance equals 1 divided by focal length. Using symbols, 1 over d sub o plus 1 over d sub i equals 1 over f. Magnification m equals image height divided by object height, which also equals negative image distance divided by object distance. Positive magnification means upright, negative means inverted. Absolute magnification above 1 means larger, below 1 means smaller. In the OpenStax sign convention here, focal length is positive for a concave mirror, image distance positive for a real image, negative for a virtual image.

Worked example for Case 1. Take focal length 15 centimeters, so C is at 30 centimeters. Place an object 45 centimeters away, beyond C. Then 1 over d sub i equals 1 over 15 minus 1 over 45, which equals 2 over 45, so d sub i equals 22.5 centimeters, between F at 15 and C at 30, as Case 1 requires. Magnification equals negative 22.5 divided by 45, or negative 0.5, so inverted and one half the height, therefore smaller. Worked example for Case 5. Use the same mirror. Place an object 10 centimeters away, inside F. Then 1 over d sub i equals 1 over 15 minus 1 over 10, or negative 1 over 30, so d sub i equals negative 30 centimeters, meaning virtual, behind the mirror. Magnification equals positive 3, so upright and three times the height, therefore larger. For an object at C, 30 centimeters, the equation gives image distance 30 centimeters and magnification negative 1. For an object at 20 centimeters, between C and F, it gives 60 centimeters and magnification negative 3.

Common Mistakes and How to Fix Them

The most frequent mistake is swapping Ray 1 and Ray 2. Remember: parallel in goes through F out, through F in goes parallel out. The second mistake is drawing the center ray as if it reflected at an angle. A ray through C meets the mirror along the normal, so it must return along the same line. The third mistake is placing F wrongly: it must be halfway between V and C. The fourth mistake is forgetting dashed extensions for a virtual image. If reflected rays spread apart and you stop there, you have not located the image. The fifth mistake is stating only part of the description. Always give type, orientation, size, and location, because real and inverted alone could describe Case 1, Case 2, or Case 3. The sixth mistake is mixing concave and convex rules. A convex mirror always gives a virtual, upright, smaller image behind the mirror for a real object. Check shape first: inward means concave, outward means convex.

Everyday and Technical Uses, Matched to the Right Case

Uses make sense only when matched to the case that produces them. A magnified upright image needs Case 5; a concentrated beam or reduced real image needs another part of the diagram. Shaving and makeup mirrors use Case 5. The face is placed close to the mirror, inside F, so the image is virtual, upright, and larger. That enlargement helps close detail work, and upright orientation keeps the view natural. The same geometry explains dental mirrors viewing teeth at magnified scale.

Reflecting telescopes use a concave mirror to collect light from distant objects and form a real image. A distant star sends effectively parallel rays, so the image forms near F, small and inverted, following the far object limit of Case 1. The telescope then magnifies that real image with further optics. A larger mirror collects more light, and a curved mirror can focus it. Vehicle headlights, torches, and searchlights use the reverse of Case 4. A source at or near F sends rays reflecting into a near parallel beam. In textbook diagrams this is shown with a concave mirror and source at F. In practice, many modern lighting reflectors use a parabolic shape, because a parabola focuses parallel rays exactly, while a spherical mirror does so only in the paraxial approximation.

Solar concentrators use convergence in the other direction: parallel sunlight is focused onto a small receiver. OpenStax gives a worked example of a parabolic trough, a concentrating collector, focusing sunlight onto a blackened pipe containing fluid, with that heated fluid then used to generate steam and electricity. A concave reflector gathers light over a wide area and concentrates it at the focus. Solar furnaces and solar cookers follow the same principle, focusing sunlight to produce heat at the focal region. As with headlights, the manufactured shape is often parabolic rather than spherical.

Practice: Draw All Five Cases on One Page

Put all five cases side by side, with the same mirror and same F and C positions in each panel, so only object position changes. Label V, F, and C, draw the object arrow, draw at least two rays, mark the image arrow, and write the four descriptors underneath. Start with Case 2, easiest to verify: same size, at C, real, inverted. Then check Case 1 and Case 3, Case 5, and Case 4 against the summary.

Frequently Asked Questions

What is a concave ray diagram mirror drawing used for?

It predicts the image formed by a concave mirror without a full calculation first. Drawing principal rays from the object tip and following their reflected paths shows whether the image is real or virtual, upright or inverted, larger or smaller, and where it sits relative to mirror, F, and C.

What are the three principal rays for a concave mirror?

They are the parallel ray, parallel to the axis then through F; the focal ray, through F then parallel to the axis; and the center ray, through C then back along the same line. Two rays locate an image, and the third provides a check.

Where is the focal point of a concave mirror?

It lies on the principal axis, halfway between vertex and center of curvature. In the paraxial approximation, focal length is one half of radius of curvature, so C is twice as far from the mirror as F.

What image forms when the object is beyond C?

The image is real, inverted, and smaller, located between F and C, in front of the mirror. As the object moves farther away, the image moves closer to F and becomes smaller.

What image forms when the object is at C?

The image is real, inverted, and the same size as the object, located at C. This symmetric case checks that F is halfway between vertex and C.

What image forms when the object is between C and F?

The image is real, inverted, and larger, located beyond C. This case gives an enlarged real image that can be projected onto a screen.

What happens when the object is at the focal point?

The reflected rays are parallel and do not meet at a finite point, so the image is described as formed at infinity, real, inverted, and highly enlarged in the limiting sense. In reverse, a source at F produces a near parallel beam, the principle behind torches, searchlights, and headlight reflectors, subject to the parabolic qualification in the uses section.

What image forms when the object is inside F?

The image is virtual, upright, and larger, located behind the mirror. Only backward extensions meet, so it cannot be projected onto a screen, but it can be seen in the mirror. This is the case used by shaving, makeup, and dental mirrors.

Can a concave mirror form both real and virtual images?

Yes. It forms a real inverted image when the object is outside F, and a virtual upright image when inside F. F is the boundary. A convex mirror is separate, noted only as a related topic.

How is a ray diagram different from the mirror equation?

A diagram shows geometry visually and locates the image by intersections or backward extensions. The mirror equation, 1 over object distance plus 1 over image distance equals 1 over focal length, gives the same location numerically, and magnification, negative image distance over object distance, gives orientation and size. Using both lets you check a visual answer with numbers, and vice versa.

Why do some diagrams mention a vertex ray?

OpenStax lists a fourth principal ray, the vertex ray, striking the vertex and reflecting symmetrically about the axis. This guide uses three rays, sufficient for every case here. The vertex ray is a valid extra check and should give the same image point.

What is the difference between a concave mirror and a convex mirror?

A concave mirror reflects from the inside of a sphere, curves inward, and can form real or virtual images depending on position. A convex mirror reflects from the outside, curves outward, and, for a real object, forms a virtual, upright, smaller image behind the mirror. Convex rules should not be applied to concave diagrams.

Sources & references

• OpenStax University Physics III, Section 2.3: Spherical Mirrors, via Physics LibreTexts. https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/02:_Geometric_Optics_and_Image_Formation/2.03:_Spherical_Mirrors
• Pearson Physics Study Guide: Spherical Mirrors, Ray Diagrams and Image Formation. https://www.pearson.com/channels/physics/study-guides/spherical-mirrors-ray-diagrams-image-formation-and