What this calculator does
The angle of incidence is the angle between an incoming ray and the normal, an imaginary line drawn perpendicular to the surface it strikes, not the surface itself. It is the standard reference angle used throughout optics, from mirrors to lenses to solar panels, precisely because measuring off the normal rather than the surface keeps the geometry consistent regardless of how the surface is tilted.
For a flat, reflective surface, the law of reflection states that the angle of reflection always equals the angle of incidence, both measured from the same normal. This calculator applies that law directly, and also reports the grazing angle (measured from the surface instead of the normal) and the total angle through which the ray is deflected, which is a common follow-up question once the basic reflection angle is known.
The formula
The angle of reflection is set equal to the angle of incidence by the law of reflection. The grazing angle is 90° minus the angle of incidence, since the normal and the surface are always perpendicular to each other. The total deflection of the ray is 180° minus twice the angle of incidence, which is the angle you would need to turn the incoming ray through to line it up with the outgoing reflected ray.
| Term | Meaning |
|---|---|
| Normal | An imaginary line perpendicular to the surface at the point the ray strikes it; all angles here are measured from the normal, not the surface. |
| Angle of incidence | The angle between the incoming ray and the normal. |
| Law of reflection | For a flat, mirror-like surface, the angle of reflection equals the angle of incidence. |
The inputs explained
| Field | What to enter |
|---|---|
| Angle of incidence (from the normal) (°) | The angle between the incoming ray and the normal, from 0° (striking the surface straight on) to 90° (skimming almost parallel to the surface). |
When to use it
Aligning a mirror or periscope
Positioning a mirror to redirect light to a specific target relies directly on the law of reflection: the mirror only needs to be angled so the desired reflection angle matches the incoming light’s angle of incidence.
Solar panel and window glare analysis
How much sunlight reflects off a glass or panel surface, rather than passing through or being absorbed, depends heavily on the angle of incidence, which is why panel tilt and window orientation are chosen with this angle in mind.
Camera flash and lighting setups
Photographers and lighting technicians angle reflective surfaces and diffusers using the same reflection law, working out where a light source needs to sit so its reflection lands exactly where it is wanted.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the reflected ray change with the angle of incidence?
A range of angles of incidence, all measured from the normal.
| Angle of incidence | Angle of reflection | Angle measured from the surface (grazing angle) | Total deflection of the ray |
|---|---|---|---|
| 0° | 0.00° | 90.00° | 180.00° |
| 15° | 15.00° | 75.00° | 150.00° |
| 30° | 30.00° | 60.00° | 120.00° |
| 45° | 45.00° | 45.00° | 90.00° |
| 60° | 60.00° | 30.00° | 60.00° |
| 75° | 75.00° | 15.00° | 30.00° |
| 89° | 89.00° | 1.00° | 2.00° |
Questions
Why is the angle measured from the normal instead of the surface?
Measuring from a line perpendicular to the surface keeps the definition consistent no matter how the surface is oriented or curved at that point. Measuring from the surface itself would make the same physical ray have a different-looking angle depending on how the surface happened to be drawn.
Does the law of reflection apply to curved mirrors too?
Yes, at the point of reflection. The normal to a curved surface changes direction from point to point, but at any single point of contact, the angle of reflection still equals the angle of incidence measured against the normal at that exact point.
What happens to the angle when the ray refracts instead of reflects?
Refraction, where a ray bends while passing into a different transparent medium rather than bouncing off the surface, follows a different relationship (Snell’s law), which depends on the refractive indices of both materials, not just the angle of incidence.
Can the angle of incidence be greater than 90°?
No. By definition it is always measured as the acute angle between the incoming ray and the normal, so it stays between 0° (straight on) and 90° (grazing along the surface).
For how a ray bends passing between two different media instead of reflecting, see the Snell’s law calculator. For the specific incidence angle at which reflected light becomes fully polarised, see the Brewster’s angle calculator.