Reflection in Mirrors: Angles, Virtual Images, and Ray Construction

What “Reflection” Means in Ray Optics

In ray optics, reflection is modeled by straight-line rays that bounce off a surface. A mirror is a surface engineered so that reflection is mostly specular (orderly), meaning incoming parallel rays leave in a predictable direction. This predictability lets us construct images with geometry.

The Law of Reflection (with Careful Angle Definitions)

Normal line and angle conventions

At the point where a ray hits a mirror, draw a line perpendicular to the surface. This perpendicular line is called the normal. All reflection angles are measured relative to the normal, not relative to the mirror surface.

• Angle of incidence θi: the angle between the incoming ray and the normal.
• Angle of reflection θr: the angle between the reflected ray and the normal.

Law of reflection

θi = θr. The incident ray, reflected ray, and the normal all lie in the same plane (the “plane of incidence”).

Step-by-step: reflecting a single ray

1. Mark the point where the ray hits the mirror.
2. Draw the normal at that point (perpendicular to the surface).
3. Measure θi from the incident ray to the normal.
4. On the other side of the normal, draw the reflected ray so that θr equals θi.

Common mistake checkpoint

If you measure angles from the mirror surface instead of from the normal, you will get the wrong geometry. Angles from the surface are complementary: θ(surface) = 90° − θ(normal).

Plane Mirrors: Virtual Images and Ray Construction Rules

What a plane mirror image is (and is not)

A plane mirror forms a virtual image: rays do not actually converge at the image location. Instead, your brain traces reflected rays backward in straight lines and perceives them as coming from a point behind the mirror.

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Ray-diagram recipe for a plane mirror (step-by-step)

1. Draw the mirror as a straight line.
2. Place the object point (or the top of an object arrow) in front of the mirror.
3. Draw at least two rays from that point to the mirror (choose convenient directions).
4. At each hit point, draw the normal and reflect each ray using θi = θr.
5. Extend the reflected rays backward behind the mirror as dashed lines.
6. The dashed extensions intersect at the image point. Repeat for another point on the object to locate the full image.

Key properties of plane-mirror images

• Image distance equals object distance: if the object is distance d in front of the mirror, the image appears distance d behind it (measured along a perpendicular to the mirror).
• Same size: magnification m = +1 (upright, not inverted).
• Laterally reversed: left-right reversal is a consequence of reflection geometry, not a “flip in depth.”

Conceptual checkpoint: why the image appears behind the mirror

After reflection, rays diverge as they travel to your eye. Your visual system assumes light travels in straight lines, so it extrapolates each ray backward. Those backward extensions meet behind the mirror, so that is where the brain locates the source. No light actually travels behind the mirror; the “behind” location is a geometric construction.

Spherical Mirrors: Concave and Convex

Curved mirrors are often approximated as parts of a sphere (spherical mirrors). Their geometry introduces special points used for ray diagrams.

Principal axis, vertex, center of curvature, and focus

• Principal axis: the line through the mirror’s center of curvature and the vertex (the midpoint of the mirror).
• Vertex V: where the principal axis meets the mirror surface.
• Center of curvature C: center of the sphere of which the mirror is a part.
• Radius of curvature R: distance VC.
• Focal point F: for spherical mirrors (paraxial rays), f = R/2.

Concave mirror: reflective surface curves inward (like the inside of a bowl). It can form real or virtual images depending on object position. Convex mirror: reflective surface bulges outward; it forms only virtual, upright, reduced images.

Principal Rays for Ray Diagrams (Curved Mirrors)

To locate images quickly, use three “principal rays.” You typically need any two to find the image point; the third acts as a check.

Concave mirror principal rays

• Parallel ray: a ray parallel to the principal axis reflects through the focus F.
• Focal ray: a ray passing through F reflects parallel to the principal axis.
• Center ray: a ray passing through C reflects back on itself (it hits the mirror along a radius, so it meets the surface normal).

Convex mirror principal rays

• Parallel ray: a ray parallel to the principal axis reflects as if it came from the focus F behind the mirror (extend the reflected ray backward to F).
• Focal ray: a ray aimed toward F behind the mirror reflects parallel to the principal axis.
• Center ray: a ray aimed toward C behind the mirror reflects back along its incoming path (use backward extensions to locate C).

Finding Image Position, Size, and Type with Ray Diagrams

Step-by-step: concave mirror image construction

1. Draw the mirror, principal axis, and mark V, F, and C (with F halfway between V and C).
2. Draw the object as an upright arrow at a chosen position on the axis.
3. From the top of the object, draw two principal rays (e.g., parallel ray and center ray).
4. Reflect each ray using the concave rules above.
5. The intersection of the reflected rays gives the image top. Drop a line to the axis to locate the image base.
6. Determine image type: if reflected rays physically intersect in front of the mirror, the image is real and typically inverted. If only backward extensions intersect behind the mirror, the image is virtual and upright.

Step-by-step: convex mirror image construction

1. Draw the mirror and principal axis; mark V. Place F and C behind the mirror (on the far side).
2. Draw the object arrow in front of the mirror.
3. From the object top, draw a parallel ray; reflect it so it diverges as if from F (extend backward to F with a dashed line).
4. Draw a ray aimed toward C (behind the mirror); reflect it back along itself (again, use dashed backward extensions).
5. The backward extensions intersect behind the mirror: that point is the virtual image top.

How to read the diagram: real vs virtual, upright vs inverted

Magnification from geometry (what “bigger” means)

Magnification compares image height to object height: m = hi/ho. In ray diagrams, you can estimate hi by measuring the image arrow relative to the object arrow. Sign conventions vary by textbook, but conceptually:

• Upright image → m is positive.
• Inverted image → m is negative.
• Enlarged → |m| > 1; reduced → |m| < 1.

Conceptual Checkpoints for Curved Mirrors

Why concave mirrors can project images onto a screen

A screen shows an image only if light rays physically converge on it. A concave mirror can make reflected rays converge to a point in front of the mirror when the object is beyond the focal point. That convergence forms a real image that can be caught on paper, a wall, or a sensor.

Why convex mirrors cannot project a real image

A convex mirror makes reflected rays diverge. Diverging rays do not meet in front of the mirror, so there is no real convergence point to place a screen. The image is always virtual, located where backward extensions meet behind the mirror.

How moving the object changes magnification (concave mirror)

Use the principal points F and C as landmarks. As you slide the object along the axis:

• Object beyond C (farther than the center of curvature): image forms between F and C, real, inverted, reduced.
• Object at C: image at C, real, inverted, same size.
• Object between C and F: image beyond C, real, inverted, enlarged (magnification grows as the object approaches F).
• Object at F: reflected rays leave parallel; the image is effectively at infinity (no sharp image on a nearby screen).
• Object inside F (closer than the focal length): image appears behind the mirror, virtual, upright, enlarged (this is the “makeup mirror” regime).

Practical Examples You Can Connect to Daily Life

Makeup/shaving mirrors (concave)

These are concave mirrors used with your face inside the focal length. Ray diagrams predict a virtual, upright, magnified image behind the mirror, making details easier to see. If you move too far away (past the focal point), the image flips to real and inverted, which feels surprising but matches the ray construction.

Rear-view and side-view mirrors (convex)

Many vehicle side mirrors are convex to provide a wider field of view. The tradeoff is that images are reduced (smaller), which is why objects appear farther away than they are. Ray diagrams show the image always forms behind the mirror, upright and diminished.

Reflective safety devices (convex and corner reflectors)

Roadside safety reflectors and bicycle reflectors are designed to send light back toward its source. Many use arrangements that effectively return rays toward the incoming direction, improving visibility at night. While not a single spherical mirror, the same reflection rule (θi = θr) governs how the device redirects headlight beams back to drivers.