Reflective Optics & Mirrors — Abridged Guide
Quick-reference guide for mirror types, equations, coatings, substrates, and selection. For the full treatment with worked examples and diagrams, see the Comprehensive Guide.
1.Introduction to Reflective Optics
Mirrors reflect light without chromatic aberration, work across the full UV–IR spectrum from a single surface, and avoid substrate absorption losses — making them essential for broadband, high-power, and large-aperture photonics systems.
When a mirror is tilted by Δθ, the reflected beam deviates by 2Δθ. This doubling effect makes mirrors highly sensitive alignment elements — account for it in beam-pointing budgets.
Mirrors are fundamental to every optical laboratory. Unlike lenses, a mirror's reflection obeys the law of reflection (\theta_i = \theta_r) at all wavelengths identically, so a single mirror surface handles ultraviolet through far-infrared with no dispersion or chromatic focal shift. This achromatic advantage drives the use of mirrors in ultrafast laser systems, broadband spectroscopy, and astronomical telescopes.
2.Mirror Types & Geometry
Focal Length of a Spherical Mirror
f = focal length (mm), R = radius of curvature (mm). Positive for concave, negative for convex.
Plane mirrors steer beams without adding optical power. Spherical mirrors focus or diverge light but introduce spherical aberration at low f-numbers. Parabolic mirrors (K = −1) eliminate spherical aberration for collimated input.
| Mirror Type | Key Property | Application |
|---|---|---|
| Plane | No optical power | Beam steering, folding |
| Spherical concave | f = R/2, SA present | General focusing, cavities |
| Parabolic concave | Zero SA on-axis | Collimation, telescopes, OAPs |
| Hyperbolic | SA-corrected with primary | Cassegrain/R-C secondaries |
3.The Mirror Equation & Image Formation
Mirror Equation
s = object distance, s' = image distance, f = focal length. All in mm; positive values are in front of the mirror.
Lateral Magnification
m < 0 → inverted image; |m| > 1 → magnified.
The mirror equation is valid for concave and convex mirrors under the paraxial approximation. Use three principal rays (parallel, focal, center-of-curvature) for graphical image construction.
Convex mirrors always produce virtual, upright, diminished images regardless of object distance. Concave mirrors produce real images when the object is beyond the focal point and virtual images when inside it.
4.Focal Length, f-Number, and NA
f-Number and NA for Mirrors
D = clear aperture diameter (mm), f = focal length (mm).
Lower f-numbers (faster mirrors) give tighter focused spots but increase aberrations. For spherical mirrors, f/4 or slower keeps spherical aberration manageable; faster than f/2 requires a parabolic surface.
The F-Number & NA Calculator on this site handles these conversions interactively for any optic, including mirrors.
→5.Spherical Aberration & Aspheric Solutions
Longitudinal Spherical Aberration
LSA = axial distance between marginal and paraxial foci (mm).
Spherical aberration scales inversely with the square of f-number. Doubling the f-number (e.g., f/2 → f/4) reduces LSA by 4×. Parabolic mirrors eliminate SA entirely for on-axis collimated light.
Conic Constant
K = 0 (sphere), K = −1 (parabola), K < −1 (hyperbola), −1 < K < 0 (prolate ellipsoid).
Off-axis parabolic mirrors (OAPs) provide aberration-free focusing with unobstructed focal access, but they are extremely sensitive to angular misalignment. Even milliradians of tilt introduce coma. For a 90° OAP, the reflected focal length is twice the parent focal length.
6.Mirror Coatings
Aluminum works UV through IR (R ~90% visible, dips at 850 nm). Silver has the highest visible/NIR reflectivity (R ~97–99% from 450 nm onward) but tarnishes. Gold excels in the IR (R >97% above 650 nm) and is chemically inert.
| Coating | Best Spectral Range | R (Visible) | R (1064 nm) | Durability |
|---|---|---|---|---|
| Protected Al | UV–NIR | ~88% | ~93% | Good |
| Protected Ag | Vis–IR | ~97% | ~99% | Moderate |
| Protected Au | NIR–Far-IR | ~60% | ~98% | Excellent |
| Dielectric HR | Laser line | >99.9% | >99.9% | Excellent |
For pulsed lasers, check the coating's damage threshold at your pulse duration and wavelength. Dielectric mirrors handle 10–100× higher fluence than metallic coatings.
7.Substrate Materials & Specifications
N-BK7 for budget applications. Fused silica for UV/high-power lasers (low CTE, high damage threshold). Zerodur or ULE for near-zero thermal expansion requirements.
| Substrate | CTE (×10⁻⁶ /K) | Cost | Best For |
|---|---|---|---|
| N-BK7 | 7.1 | Low | General purpose |
| Fused silica | 0.55 | Moderate | Lasers, UV |
| Zerodur | ~0.05 | High | Thermal stability |
| ULE | ~0.03 | Very high | Space, LIGO-class |
Total Integrated Scatter
σ = RMS surface roughness, λ = wavelength. Surface quality grades: λ/4 (standard), λ/10 (precision), λ/20 (reference).
Surface roughness matters more at shorter wavelengths. A mirror with 10 Å RMS roughness scatters 4× more at 400 nm than at 800 nm.
8.Aberrations in Mirror Systems
Beyond spherical aberration (on-axis), mirrors exhibit coma, astigmatism, field curvature, and distortion for off-axis points. Coma is the dominant field aberration for parabolic mirrors and limits field of view.
Ritchey-Chrétien telescopes (two hyperbolic mirrors) eliminate both spherical aberration and coma — making them the design of choice for wide-field astronomical imaging. The Hubble Space Telescope uses this configuration.
9.Practical Considerations
Beam Deviation
Mirror tilt produces 2× beam deviation. In multi-mirror beam paths, angular errors accumulate — minimize the number of steering mirrors for best pointing stability.
Ghost reflections from the back surface of metallic mirrors can be mitigated with wedged substrates, AR-coated back surfaces, or absorbing substrate materials. Always check for ghosts when commissioning a new beam path.
10.Mirror Selection Workflow
The selection sequence is: wavelength range → coating type → mirror geometry → substrate material → surface quality → size and mounting → damage threshold verification.
When in doubt between mirror geometries: use flat mirrors for steering, spherical concave for focusing at f/4 or slower, and parabolic (or OAP) for anything faster than f/4 or where broadband diffraction-limited performance matters.
Continue Learning
Comprehensive Mirrors Guide →Mirror Equation Calculator →F-Number & NA Calculator →Mount Sensitivity Calculator →
The Comprehensive Guide includes 7 worked examples, 6 SVG diagrams, and 10 references.