How this instrument works
The angle of incidence and the angle of reflection are both measured from the normal — the line perpendicular to the reflecting surface at the point a ray strikes it — never from the surface itself. The law of reflection states the two are equal: θ_r = θ_i. A beam arriving 20° off the normal leaves 20° off the normal on the opposite side of that line, and a beam coming in nearly parallel to the surface, close to a 90° grazing pass, leaves at that same steep grazing angle rather than being flattened or steepened by the bounce.
The equality follows from Fermat's principle: light travels between two fixed points by the path that takes the least time. For a single bounce off a flat mirror, among every point on that mirror the beam could strike, travel time is shortest exactly where the incoming and outgoing rays make equal angles with the normal. Huygens' wavefront construction reaches the identical result by pure geometry, since a flat mirror simply flips a wavefront's direction of travel without distorting its shape.
The law describes specular reflection, where the surface is flat at the scale of the light's wavelength; a frosted window or a sheet of paper obeys the same equality at every microscopic facet but scatters the reflected rays in visibly different directions because those facets tilt every which way, which is why the surface looks matte rather than mirror-bright. Laser technicians aligning an interferometer, heliostat engineers aiming sunlight at a solar-thermal tower, and cinematographers angling a bounce card all lean on this one equality to predict exactly where a reflected beam lands.
- Enter the Angle of incidence — the angle between the incoming ray and the surface normal, not the mirror face itself, in degrees or radians.
- Read the Angle of reflection — the instrument returns it instantly, since the law of reflection sets it equal to whatever you entered.
- Switch either field's unit menu to radians if your CAD drawing, ray-tracing script, or lab notebook measures angles that way instead.
- Keep the Angle of incidence at zero or above; a negative entry is flagged, since the angle here is a magnitude measured out from the normal.
Worked example — a 35° mirror strike
Aim a laser at a flat, front-surfaced mirror so the beam strikes 35° off the normal — the perpendicular line through that point on the glass, not the angle read against the mirror's own face. Enter 35 into Angle of incidence and the Angle of reflection reads 35° as well, because θ_r = θ_i leaves no other value on the table. On an optical bench building a Michelson interferometer, that predictable 35° return is exactly what lets a technician park the second mirror precisely where the reflected beam needs to land.
Switch the unit menu to radians and the same geometry reads 0.610865 rad in and 0.610865 rad out — 35° expressed as an arc-length ratio, π ⁄ 180 per degree, rather than a fraction of a full turn. That match, to the display's precision, is the entire content of the law: no scaling, no offset, just a strict equality that has been part of optics since antiquity and that every specular mirror, from a bathroom mirror to a spacecraft's laser-ranging retroreflector, still obeys today.
Questions
Why is the angle measured from the normal instead of the mirror's surface?
Because the normal — the line perpendicular to the surface at the point of contact — stays consistent regardless of how a surface is tilted, curved, or bent, while a reading taken against the surface itself would shift with every change of shape. Optics has measured this way for millennia, and every later law, including Snell's law of refraction, follows the same normal-first convention.
Does the law of reflection hold for curved mirrors too?
Yes, applied locally. At the exact point a ray strikes a curved mirror, the relevant normal is perpendicular to the tangent plane at that point, and θ_r still equals θ_i measured from it. Parabolic telescope mirrors and satellite dishes are shaped so that this local reflection redirects parallel incoming rays through a single focal point.
What happens to the law at a rough or frosted surface?
It still holds at the microscopic level — every tiny facet reflects light with θ_r equal to θ_i measured from that facet's own local normal. Because the facets tilt in every direction, the reflected rays scatter across a wide range of macroscopic angles instead of bouncing off in one direction, which is what makes a surface look matte rather than mirror-bright even though the underlying law never changes.
Does the angle of incidence tell me how much light gets reflected?
No — it only fixes the direction of the reflected ray, not its brightness. How much light reflects versus gets absorbed or transmitted is governed separately by the Fresnel equations, which depend on the angle, the refractive indices of both materials, and the light's polarization; that reflected fraction typically climbs sharply as the angle approaches a 90° grazing pass.
How is this different from Snell's law of refraction?
Reflection keeps the ray in the same medium and simply flips its direction, so θ_r = θ_i with no material property involved. Refraction sends the ray into a second medium and bends it according to n₁ sin θ₁ = n₂ sin θ₂, where the two refractive indices do work that is entirely absent from the reflection formula. A glass pane produces both effects at once from a single incoming beam — a faint reflected image and a bent transmitted one.
Can the angle of incidence be 90°, or negative?
Not quite 90° in practice, and never negative here. A ray traveling exactly along the surface never actually strikes it, so 90° is a limit the geometry approaches but does not reach, while a negative entry trips the instrument's check, since the angle of incidence is defined as a non-negative magnitude measured out from the normal, not a signed direction.