Example data table
| Mode | Input | Main output | Notes |
|---|---|---|---|
| Given incidence | Incidence = 30° (from normal) | Reflection = 30°, Separation = 60° | Law of reflection: i = r |
| Given reflection | Reflection = 25° (from normal) | Incidence = 25°, Separation = 50° | Same reference for i and r |
| Given separation | Between rays = 80° | Incidence = 40°, Reflection = 40° | Separation = 2i |
| Mirror rotation | Rotation = 4° | Reflected deflection = 8° | Deflection = 2× rotation |
| Two mirrors | Angle between mirrors = 45° | Estimated images ≈ 7 | When 360/θ is integer: n ≈ (360/θ) − 1 |
Formula used
- Law of reflection (plane mirror): i = r, where angles are measured from the normal.
- Separation between incident and reflected rays: S = 2i (from the normal).
- Mirror rotation effect: if the mirror rotates by θ, the reflected ray rotates by 2θ.
- Two mirrors (ideal estimate): let m = 360° / θ. If m is integer, images ≈ m − 1 (bisector case). Otherwise images ≈ ⌊m⌋.
- Surface vs normal conversion: θ_normal = 90° − θ_surface.
How to use this calculator
- Select a calculation mode that matches your known value.
- Choose your input unit (degrees or radians) and angle reference.
- Enter the required angle value(s), then press Calculate.
- Review results shown above the form, below the header.
- Use Download CSV or Download PDF to export results.
Practical notes
- For most optics problems, angles are measured from the normal.
- If your problem statement gives angles from the surface, switch the reference.
- Real mirrors are not perfect; roughness and thickness can change what you see.
Mirror angle guide
1) What the “mirror angle” means
For a plane mirror, the important angle is measured between the ray and the normal, which is perpendicular to the mirror at the hit point. In simple reflection, this “from-normal” angle stays between 0° and 90°. Angles near 0° are near-straight return, while angles near 90° are grazing paths.
2) Incidence equals reflection
The key rule is i = r. If a beam arrives at 30° to the normal, it leaves at 30° on the other side. This symmetry lets the calculator solve many cases with one input.
3) Converting surface angles to normal angles
Some problems give angles from the mirror surface. Convert with θnormal = 90° − θsurface. Example: 60° to the surface becomes 30° to the normal, so the reflection is also 30°.
4) Angle between incident and reflected rays
The separation between the incoming and outgoing directions is S = 2i when i is measured from the normal. With i = 40°, the rays are 80° apart. At i = 0°, S = 0°; near 90°, S approaches 180°. If you know S, then i = S/2.
5) Mirror rotation: the 2× steering effect
Rotating a plane mirror by θ rotates the reflected ray by 2θ. A 2° mirror tweak produces a 4° beam change, and 5° yields 10°. This “double-angle” behavior is used in alignment and scanning.
6) Two mirrors: quick image count estimate
With two plane mirrors at angle θ, define m = 360°/θ. If m is an integer and the object is on the bisector, images are often about m − 1. For θ = 45°, m = 8, so the estimate is 7 images.
7) Practical tips and common pitfalls
Most mistakes come from mixing references: “from surface” vs “from normal”. Keep units consistent (degrees vs radians), and increase decimal precision for radians to reduce rounding. Typical uses include optics homework, periscope layouts (often 45° mirrors), and documenting lab settings via CSV/PDF exports. Check inputs stay within valid ranges.
FAQs
1) Why is the reflection angle equal to the incidence angle?
For an ideal plane mirror, the normal splits the incoming and outgoing rays symmetrically. That geometry gives the law of reflection: i = r, when both angles are measured from the normal.
2) What is the “normal” line?
The normal is an imaginary line drawn perpendicular to the mirror at the point of incidence. It is the reference line used in most optics formulas and keeps angle rules consistent across different diagrams.
3) Can I enter angles measured from the surface?
Yes. Select the “Measured from the surface” option. The calculator converts with θnormal = 90° − θsurface and then applies the same reflection equations.
4) Why does the angle between rays equal 2i?
The incident ray is i from the normal on one side, and the reflected ray is i on the other side. Adding equal angles produces the full separation: S = 2i.
5) Does mirror rotation always change the beam by 2×?
For a plane mirror and small rotations, yes. When the mirror turns by θ, the normal turns by θ, so the reflected direction shifts by 2θ. Large setups may have extra geometry constraints.
6) How should I use radians here?
Choose “Radians (rad)” and enter your angle in radians. Results are returned in radians with your selected precision, while internal checks use degree equivalents to keep the valid-angle limits consistent.
7) Are two-mirror image counts exact in real life?
They are ideal estimates. Mirror size, edge blocking, surface defects, and object position can reduce visible images. Use the value as a guideline, especially when 360°/θ is not an integer.