Short answer
- A convex mirror light ray diagram shows how light leaves an object, reflects from a mirror that bulges outward toward the object, and then spreads apart. Draw at least two principal rays from the top of the object and extend their reflected paths backward behind the mirror with dashed lines. Where those dashed extensions meet is the top of the image. For an object at any finite distance in front of a convex mirror, that meeting point is always behind the mirror, between the mirror surface and the focal point. The image is therefore always virtual, upright, and diminished, which means smaller than the object. That combination lets a convex mirror show a wider scene than a flat mirror of the same size, while making each object look smaller.
What a convex mirror is
A convex mirror is a curved mirror whose reflecting surface bulges outward toward the incoming light, like the outside of a spoon or the outside of part of a sphere. University Physics Volume 3 describes a convex mirror in exactly this way: the reflecting surface is the outer side of the sphere.
Because the surface curves outward, parallel rays that strike it do not come together after reflection. They spread apart, or diverge. That is why a convex mirror is often called a diverging mirror. The reflected rays themselves never meet in front of the mirror. The image is found instead by asking where the reflected rays appear to come from when their paths are extended backward behind the mirror.
A ray diagram does not draw every ray leaving an object. Light leaves each point on an object in many directions, and drawing all of those rays would fill the page. Instead, it selects a small number of special rays whose paths after reflection are easy to construct. Those rays are called principal rays. If two principal rays are drawn correctly, their reflected paths, or their backward extensions, locate the image of the point from which they started.
The parts you need before you draw
Draw five labeled parts first, before any rays.
First, draw the mirror as a short curved arc that bulges toward the object. In the usual layout, the object stands on the left and the mirror stands on the right, bulging toward the left. No light travels on the right side, behind the mirror.
Second, draw the principal axis, also called the optical axis: a straight horizontal line through the middle of the mirror. It passes through the center of curvature and through the vertex of the mirror, as described in University Physics Volume 3.
Third, mark the vertex, labeled V: the center point of the mirror surface, where the principal axis meets the mirror.
Fourth, mark the center of curvature, labeled C. Imagine completing the mirror arc into a full sphere. The center of that sphere is the center of curvature. For a convex mirror, C lies behind the mirror, on the side away from the object. The distance from V to C is the radius of curvature, labeled R.
Fifth, mark the focal point, labeled F. It lies on the principal axis, halfway between V and C, so the focal length f is half of R in the small angle approximation used in standard textbook ray tracing. For a convex mirror, F also lies behind the mirror. Because F is behind the mirror, light never actually passes through it. It is a virtual focal point. Parallel rays after reflection only appear to come from F.
A common early mistake is to place F and C in front of the mirror. In a convex mirror diagram, the order from the mirror outward behind it is V, then F, then C.
The four principal rays
University Physics Volume 3 lists four principal rays whose reflections are easy to construct. All four start at the same point on the object, usually the tip of an upright arrow that represents the object. You need only two of them to locate the image, but knowing all four helps you check your work.
Principal ray 1 starts at the tip of the object and travels parallel to the principal axis toward the mirror. After reflection, it travels away from the axis, and its backward extension passes through F behind the mirror. Draw the incoming ray as a solid line, the reflected ray as a solid line leaving the mirror and moving away from the axis, and a dashed line from the reflection point backward through F. That dashed line is not a path taken by light. It is the apparent path, the line along which the reflected light appears to travel.
Principal ray 2 starts at the tip of the object and travels toward F behind the mirror. It does not reach F, because the mirror stops it first. After reflection, it travels parallel to the principal axis.
Principal ray 3 starts at the tip of the object and travels toward C behind the mirror. Because this ray travels along a line through the center of the sphere, it strikes the mirror at normal incidence, which means it strikes the surface squarely, along the radius. It is therefore reflected back along the same line from which it came.
Principal ray 4 starts at the tip of the object and strikes the vertex V. It is reflected symmetrically about the principal axis: the angle it makes with the axis on the way in equals the angle it makes with the axis on the way out, on the opposite side of the axis.
Use solid lines for real paths in front of the mirror and dashed lines for apparent paths behind the mirror. The image is formed where dashed lines meet, not where solid lines meet. If your solid reflected rays appear to meet in front of the mirror, something has gone wrong, because reflected rays from a convex mirror diverge in front of the mirror and never meet there.
How to draw the diagram step by step
Take an upright arrow object standing in front of a convex mirror, at a finite distance from the mirror. Its base sits on the principal axis, and its tip sits above the axis.
Step 1. Draw the mirror arc bulging toward the object, draw the principal axis through its middle, and mark V on the mirror, F behind the mirror, and C farther behind the mirror.
Step 2. Draw the object as an upright arrow, with its base on the principal axis and its tip above the axis. Label the base P and the tip Q, following the textbook convention, if that helps you keep track of the points.
Step 3. From tip Q, draw principal ray 1 parallel to the principal axis to the mirror. Reflect it away from the axis, and extend it backward with a dashed line through F.
Step 4. From the same tip Q, draw principal ray 2 toward F behind the mirror, stopping at the mirror surface. Reflect it parallel to the principal axis, away from the mirror.
Step 5. Find where the two dashed extensions meet behind the mirror. That meeting point is the tip of the image, labeled Q prime. It will lie between V and F, above the principal axis.
Step 6. Complete the image. The base of the image, labeled P prime, lies on the principal axis directly below Q prime. Draw the image as a smaller upright arrow from P prime up to Q prime. It is upright because Q prime is on the same side of the axis as Q, and it is smaller because Q prime is closer to the axis than Q is.
Step 7. Check with a third ray if you have room. Draw principal ray 3 from Q toward C, reflect it back along the same line, and confirm that its backward extension also passes through Q prime. If it does not, recheck the positions of F and C and the direction of each reflected ray.
The diagram for a distant object
When the object moves farther from the mirror, the diagram keeps the same structure, but the image moves closer to the mirror and becomes smaller. In the limiting case of an object at infinity, the rays arriving at the mirror from any one point on the object are effectively parallel to each other. A ray parallel to the principal axis reflects as if it came from F, and the backward extensions meet at F itself. The image therefore shrinks to a dot at the focal point, behind the mirror. Physics LibreTexts states this limit directly: for a convex mirror, if the object is at infinity, the image will be a dot on the focal point.
This limiting case is a useful check. A very distant object must give a small image close to the mirror, approaching F as the distance grows. An object very close to the mirror must give a larger image, closer to the mirror surface, though still smaller than the object itself.
Why the image is always virtual, upright, and diminished
An image is called real when light rays actually pass through the image point. An image is called virtual when light rays only appear to come from the image point, because their backward extensions pass through it. In a convex mirror, reflected rays diverge in front of the mirror, so they never pass through a common point in front of the mirror. The only common point is found by extending them backward behind the mirror, where no light actually travels, because the mirror surface blocks the path.
That is why a convex mirror image cannot be projected onto a screen. A screen in front of the mirror would receive the diverging rays spread out over a wide area, not brought together at a point. A screen behind the mirror would receive no reflected light at all. The eye, however, can see a virtual image, because the eye traces diverging rays backward in the same way the diagram does.
The image is upright because the backward extensions meet on the same side of the principal axis as the object tip, so the image arrow points the same way as the object arrow. Inverted would mean the top of the image is on the opposite side of the axis, which would require the backward extensions to cross the axis in the vertical sense. That does not happen here.
The image is diminished, or smaller than the object, because the meeting point is closer to the axis than the object tip is. The mirror equation gives the same result: with the sign convention in University Physics Volume 3, focal length is negative for a convex mirror, image distance is negative for a virtual image, and magnification equals image height divided by object height, which also equals negative image distance divided by object distance. For a real object in front of a convex mirror, magnification is positive, which confirms an upright image, and its absolute value is less than 1, which confirms a diminished image.
Size still changes with object distance. As the object moves closer to the mirror, the image also moves closer to the mirror and grows larger, approaching the size of the object but never reaching it for a real object at a finite distance. As the object moves farther away, the image moves closer to F and shrinks. Physics LibreTexts describes this movement in the same terms: as the object moves toward the mirror, the image also moves toward the mirror and increases in size.
Field of view: why a convex mirror shows more of the scene
Field of view means the angular width of the scene that can be seen in the mirror from a given viewing position. A convex mirror shows a wider field of view than a flat mirror of the same size because its outward curve reflects rays that arrive from directions farther off to the sides. For a flat mirror, only rays from a relatively narrow set of directions can strike the mirror and then reach the eye. For a convex mirror, the curved surface tilts outward toward the edges, so rays from objects farther to the side can still strike the surface at an angle that reflects them toward the eye.
The price of that wider view is the diminished image: more of the scene is compressed into the same mirror area, so each object occupies less of the mirror and looks smaller. A wider view helps a viewer notice that something is present in a side region that a flat mirror would miss. A smaller image makes detail harder to read and distance harder to judge from the image alone. A convex mirror is therefore best treated as a presence and direction aid, not as a precise measuring tool.
Everyday uses explained by the diagram
Vehicle mirrors are the most familiar use. Physics LibreTexts notes that convex mirrors provide a wide angle view and an upright image, with benefits in rearview mirrors, in store customer monitors, and for viewing large areas like intersections and parking lots. In a vehicle, a convex side mirror lets the driver see more of the lanes beside and behind the vehicle than a flat mirror of the same size would show. The upright image keeps the scene easy to read at a glance. The diminished image is the cost: objects look smaller, and their distance is harder to judge from the mirror image alone, so a driver should still check directly and use other mirrors and checks before changing lanes.
Security mirrors in shops use the same principle. A convex mirror mounted high in a corner can show a wide area of the shop floor, including aisles that would otherwise be hidden from a single viewing point. Staff can see movement across a broad area, even though individual objects and people look small. The mirror does not record anything by itself. It widens what can be seen from one place.
Blind spot mirrors are small convex mirrors added to a vehicle mirror or mounted separately to cover a side region that the main mirror misses. Their small size is possible precisely because a convex surface compresses a wide scene into a small area. The same compression explains their limit: a small blind spot mirror shows that something is present in that side region, but it shows little detail, and it should not be treated as a complete view of the road.
Mirrors at road junctions, parking lot exits, and building corners work the same way. A convex mirror placed where two paths meet lets a driver or pedestrian see around a corner without stepping into the path of oncoming movement. It shows an upright, diminished view of the approaching area, enough to reveal that someone or something is approaching, even if it is not enough to judge exact speed or distance. The value is early warning across a wide angle, not precise measurement.
In each use, the three image properties work together. Virtual means the image appears behind the mirror surface, where the viewer looks. Upright means the scene reads in its normal orientation. Diminished means the scene is compressed, which widens the view.
The mirror equation, worked through
Ray diagrams give the shape of the answer. The mirror equation gives the numbers. In the form used by University Physics Volume 3, 1 divided by object distance plus 1 divided by image distance equals 1 divided by focal length. Magnification equals image height divided by object height, which also equals negative image distance divided by object distance. Distances are measured from the vertex V. Focal length is negative for a convex mirror, and image distance is negative for a virtual image.
Worked example 1 follows the example in Physics LibreTexts. A convex mirror has a radius of curvature of 40.0 centimeters, so its focal length is negative 20.0 centimeters, because focal length is half the radius of curvature and carries a negative sign for a convex mirror. An object is placed 1000.0 centimeters in front of the mirror. Using the mirror equation, 1 divided by 1000.0 plus 1 divided by the image distance equals 1 divided by negative 20.0. Solving gives an image distance of negative 19.6 centimeters. The negative sign means the image is behind the mirror and virtual. Magnification equals 19.6 divided by 1000.0, or 0.0196, which is 1 divided by 51. The image is therefore reduced by a factor of 51, upright because magnification is positive, and virtual because the image distance is negative. In a ray diagram, this distant object gives a tiny image very close to F, which matches the result: 19.6 centimeters is just inside the focal length of 20.0 centimeters.
Worked example 2 uses round numbers for a closer object. A convex mirror has a focal length of negative 20 centimeters, and an object stands 60 centimeters in front of it. The mirror equation gives 1 divided by 60 plus 1 divided by the image distance equals 1 divided by negative 20. Rearranging, 1 divided by the image distance equals negative 1 divided by 20 minus 1 divided by 60, which is negative 4 divided by 60, or negative 1 divided by 15. The image distance is therefore negative 15 centimeters, between V and F, as the diagram requires. Magnification equals 15 divided by 60, or 0.25. The image is upright and one quarter of the height of the object. The closer object gives a larger image than the distant object gives, yet still diminished and still between V and F.
Sign discipline matters. If the negative sign on the focal length is dropped, the mirror equation will place the image in front of the mirror, which contradicts the ray diagram. Keep the diagram and the equation together: the diagram shows where the image must be, and the equation must agree with it.
Common mistakes
Placing F and C in front of the mirror is the first mistake. Both points lie behind a convex mirror. Drawing the reflected rays as if they meet in front of the mirror is the second mistake: reflected rays diverge in front of the mirror, and only their dashed backward extensions meet, behind the mirror. Drawing the image in front of the mirror, larger than the object, or inverted is the third mistake: none of those outcomes matches the geometry for a real object in front of a convex mirror. Drawing only one ray is the fourth mistake: one ray gives a line, not a point, and at least two principal rays are needed to fix the image tip. Confusing F with C is the fifth mistake: F is halfway between V and C, and C is twice as far behind the mirror as F is. Forgetting the small angle approximation is the sixth mistake: standard diagrams assume rays close to the axis and a mirror small compared with its radius of curvature.
FAQ
What is a convex mirror light ray diagram?
It is a drawing that uses selected rays, called principal rays, to locate the image formed by a convex mirror. Solid lines show real ray paths in front of the mirror, and dashed lines show the backward extensions behind the mirror where the reflected rays appear to come from. The image tip is where at least two dashed extensions meet.
Why is the image in a convex mirror always virtual?
Reflected rays from a convex mirror diverge in front of the mirror and never actually pass through a common point there. Their backward extensions meet behind the mirror, where light does not travel. An image located by backward extensions, rather than by real rays passing through the point, is virtual by definition.
Why is the image always upright and diminished?
It is upright because the backward extensions meet on the same side of the principal axis as the object tip. It is diminished because the meeting point is closer to the axis than the object tip is, so the image height is smaller than the object height. The mirror equation gives the same result: magnification is positive and less than 1 in absolute value.
Where is the image located in a convex mirror?
For an object at any finite distance in front of a convex mirror, the image lies behind the mirror, between the vertex V and the focal point F. As the object moves farther away, the image moves toward F and shrinks. As the object moves closer, the image moves toward V and grows, while still remaining smaller than the object. For an object at infinity, the image is a dot at F.
How many rays do you need to draw a convex mirror ray diagram?
At least two principal rays from the same point on the object, usually the tip. Two rays fix the image point as the intersection of their backward extensions. A third or fourth ray is a useful check, because all correctly drawn principal rays must agree on the same image point.
What is the difference between the focal point and the center of curvature?
The center of curvature C is the center of the sphere from which the mirror surface is taken, and the focal point F lies halfway between the vertex V and C, on the principal axis behind the mirror. Both points lie behind a convex mirror. A ray toward C reflects back along the same line, a ray parallel to the axis reflects as if it came from F, and a ray toward F reflects parallel to the axis.
Why do convex mirrors show a wider view than flat mirrors?
A convex mirror curves outward, so it can reflect toward the eye rays that arrive from directions farther to the sides than a flat mirror of the same size could reflect. That wider set of directions compresses more of the scene into the same mirror area, which is why each object looks smaller. The wider view and the smaller image are two sides of the same geometry.
Do convex mirrors make objects look farther away?
A diminished image can be read as a more distant object, because a smaller image is easily mistaken for a more distant one. The diagram does not by itself prove how any particular driver will judge distance, and distance should not be judged from a convex mirror image alone. The safe reading is that the image is smaller, and smaller images make distance judgment less reliable, which is why direct checks remain important.
Can a convex mirror ever form a real image of a real object?
No, not for a real object placed in front of the mirror in the usual arrangement. Reflected rays diverge, so they cannot meet in front of the mirror to form a real image. The image is virtual for every finite object distance, and it approaches a dot at F for an object at infinity.
Is a convex mirror diagram the same as a concave mirror diagram?
No. A convex mirror bulges toward the object, has its focal point and center of curvature behind the mirror, and always gives a virtual, upright, diminished image for a real object. The concave mirror article is a separate article, and it covers a mirror that curves inward, with different image outcomes depending on object position.
Sources & references
- Ling, Samuel J., Jeff Sanny, and William Moebs. University Physics Volume 3, chapter on Spherical Mirrors. UCF Pressbooks edition. https://pressbooks.online.ucf.edu/osuniversityphysics3/chapter/spherical-mirrors/
- Physics LibreTexts. Convex Mirrors, section 9.2.6, in Physical Science for Educators, Volume 2. https://phys.libretexts.org/Courses/Coalinga_College/Physical_Science_for_Educators_Volume_2/09%3A_Reflections_and_Refraction_of_Waves/9.02%3A_Optics/9.2.06%3A_Convex_Mirrors
