Ray diagrams for mirrors show how light reflects to form images. They are important because they let you predict where an image appears, how large it is, whether it is upright or inverted, and whether it is real or virtual. Concave mirrors can form several different image types depending on object position, while convex mirrors always form smaller upright virtual images.
These diagrams are used in telescopes, headlights, shaving mirrors, security mirrors, and many optical instruments.
The method uses a few principal rays whose paths are easy to draw. For spherical mirrors, the focal point F is halfway between the mirror and the center of curvature C, so f = R/2. A ray parallel to the principal axis reflects through the focal point for a concave mirror, while for a convex mirror it reflects as if it came from the focal point behind the mirror.
Where reflected rays actually meet gives a real image, and where their backward extensions appear to meet gives a virtual image.
Understanding Physics: Ray Diagrams for Mirrors
Every ray diagram begins with the law of reflection. The angle at which a ray arrives equals the angle at which it leaves. Both angles are measured from a line called the normal, which is perpendicular to the mirror surface at the point where the ray strikes.
On a curved mirror, the normal changes from place to place. For a spherical mirror, each normal points toward the center of the sphere that the mirror came from. This is why the center of curvature is useful.
The familiar principal rays are shortcuts based on this geometry. They work best for rays close to the main axis.
Rays far from the axis do not always meet at exactly one point. This spreading is called spherical aberration, and it makes real mirrors less perfect than simple diagrams suggest.
A good construction starts with a clear principal axis, a mirror line, and an object arrow placed upright on the axis. Mark the focal point and center of curvature at the correct relative distances before drawing rays. Draw at least two rays from the tip of the object.
Two reflected rays are enough to locate the image because two straight paths meet at one location. A third ray is useful as a check. Use a ruler and keep ray arrowheads clear.
The image tip is found where the reflected rays meet, or where their dotted backward extensions meet. Then draw the image arrow down to the axis.
Its direction shows whether it is upright or inverted. Its height compared with the object shows the magnification.
The position of a concave mirror object can produce sudden changes in the diagram. When an object is beyond the center of curvature, its image is between the center and the focus. As the object moves toward the focus, the image moves farther away and grows.
At the focal point, reflected rays leave parallel, so they do not form an image at a finite distance. This case often causes mistakes in calculations because the image distance becomes extremely large. When the object is inside the focal length, the reflected rays spread apart.
Extending them backward gives an upright virtual image behind the mirror. A face seen in a close shaving mirror is an everyday example of this arrangement.
Equations are useful for checking a drawing, but they need a consistent sign convention. Many courses treat distances in front of a mirror as positive and distances behind it as negative. Other courses use a different convention, so students should follow the one their teacher gives.
A negative image distance usually indicates a virtual image in the common convention. A positive magnification means upright, while a negative magnification means inverted. Do not rely only on the final number.
Sketching first helps reveal impossible answers, such as a convex mirror producing an inverted image. In practical devices, mirrors have limited size, so some light misses the surface. Wider mirrors collect more rays and can make an image brighter, though they do not change the basic ray rules.
Key Facts
- Mirror equation: 1/f = 1/do + 1/di
- Magnification equation: m = hi/ho = -di/do
- For a spherical mirror, f = R/2, where R is the radius of curvature.
- Concave mirrors have a real focal point in front of the mirror and can form real or virtual images.
- Convex mirrors have a virtual focal point behind the mirror and always form upright, reduced, virtual images.
- A real image forms where reflected rays actually meet, while a virtual image forms where reflected rays only appear to originate.
Vocabulary
- Principal axis
- The straight reference line that passes through the mirror's vertex, focal point, and center of curvature.
- Focal point
- The point where rays parallel to the principal axis converge after reflection, or appear to diverge from after reflection.
- Center of curvature
- The center of the sphere from which a spherical mirror is a small section.
- Real image
- An image formed where reflected light rays actually meet and that can be projected onto a screen.
- Virtual image
- An image formed where reflected rays appear to come from and that cannot be projected onto a screen.
Common Mistakes to Avoid
- Drawing convex mirror rays as if they meet in front of the mirror is wrong because convex mirrors make reflected rays diverge, so the image is found by extending rays backward behind the mirror.
- Forgetting that the focal point is halfway to the center of curvature is wrong because spherical mirrors follow f = R/2, not f = R.
- Using the same image description for every concave mirror object position is wrong because a concave mirror changes image type when the object moves inside F, between F and C, at C, or beyond C.
- Ignoring sign conventions in the mirror equation is wrong because the sign of f and di determines whether the mirror and image are real or virtual.
Practice Questions
- 1 A concave mirror has focal length 10 cm. An object is placed 30 cm in front of the mirror. Use 1/f = 1/do + 1/di to find the image distance, then state whether the image is real or virtual.
- 2 A convex mirror has focal length -15 cm. An object 6 cm tall is placed 45 cm in front of the mirror. Find the image distance and magnification, then calculate the image height.
- 3 A student places an object between the focal point and a concave mirror. Explain why the image is virtual, upright, and enlarged using the behavior of reflected rays.