Calculator
Example Data Table
| Case | Inputs | Example Output |
|---|---|---|
| Energy to Wavelength | 8 keV | 1.5498 Å |
| Bragg Angle | d = 3.1356 Å, λ = 1.5406 Å, n = 1 | θ ≈ 14.22° |
| Bragg Wavelength | d = 3.1356 Å, θ = 14.22°, n = 1 | λ ≈ 1.5405 Å |
| Critical Angle | δ = 3.7 × 10-6 | θc ≈ 2.7203 mrad |
| Mirror Footprint | Beam height = 0.2 mm, angle = 3 mrad | 66.6668 mm |
Formula Used
Energy and wavelength: λ(Å) = 12.3984198433 / E(keV)
Photon frequency: f = E / h
Photon momentum: p = E / c
Bragg law: nλ = 2d sinθ
Critical angle estimate: θc ≈ √(2δ)
Zone plate focus: f = r² / (nλ)
Mirror footprint: L = h / sinα
How to Use This Calculator
Choose the calculation mode first. Each mode reveals only the fields needed for that optics task.
Enter values in the shown units. Use keV for energy, angstroms or nanometers for wavelength, and the listed angle units.
Press the calculate button. The result appears below the header and above the form.
Review the result table. Then export the current output as CSV or PDF when needed.
Use Bragg modes for diffraction work, the critical angle mode for grazing incidence checks, and the zone plate mode for x ray focusing estimates.
X Ray Optics Calculator Overview
Why x ray optics calculations matter
X ray optics studies how high energy photons behave in real systems. Their wavelengths are short. Their interaction with matter is weak and angle dependent. That makes optical design different from visible light design. A focused calculator helps students, researchers, and beamline users work faster.
What this calculator can solve
This x ray optics calculator supports common beamline and diffraction tasks. You can convert photon energy to wavelength. You can reverse the process from wavelength to energy. You can solve Bragg reflection conditions. You can estimate critical angle values for grazing incidence mirrors. You can also evaluate zone plate focus and mirror footprint length.
Bragg law and diffraction planning
Bragg diffraction is central in crystallography and monochromator design. The relation is nλ = 2d sinθ. When spacing and wavelength are known, the Bragg angle follows directly. When angle and spacing are known, the supported wavelength becomes clear. The calculator also reports related energy values. That helps compare sources, crystals, and scan settings.
Critical angle and mirror design
Critical angle matters in x ray mirrors and total external reflection. X rays usually reflect only at very small grazing angles. The refractive index decrement controls that limit. A quick estimate helps with mirror alignment and acceptance checks. It also helps you screen coating choices during early design work.
Zone plates, footprints, and practical setup
Zone plates act as diffractive x ray lenses. Their focal length depends on outer radius, wavelength, and diffraction order. Small changes in wavelength can shift the focus strongly. Fast calculations help when planning microscopy, imaging, and experimental geometry.
Mirror footprint length is also important. As the grazing angle becomes smaller, the illuminated length grows. That affects mirror size, heat load distribution, and alignment tolerances. A footprint estimate helps prevent clipping and supports better hardware choices.
Good unit handling matters in x ray work. Energies are often given in keV. Wavelength may appear in angstroms or nanometers. Angles may be written in degrees or milliradians. This calculator keeps those conversions clear. That reduces mistakes in notebooks, spreadsheets, and instrument setup sheets.
Use this page when you need reliable x ray optics numbers without manual repetition. Enter your values, pick the right model, and review the generated results. Then export the output for lab notes, reports, or coursework. The workflow is simple, but the physics remains accurate and useful.
FAQs
1. What does this x ray optics calculator do?
It solves several common optics tasks. These include energy to wavelength conversion, wavelength to energy conversion, Bragg law calculations, critical angle estimates, zone plate focus, and grazing mirror footprint length.
2. Which wavelength relation is used here?
The calculator uses λ(Å) = 12.3984198433 / E(keV). This is a standard photon relation for converting x ray energy into wavelength in angstroms.
3. Why are x ray mirror angles so small?
X rays reflect efficiently only at very small grazing angles. At larger angles, reflectivity drops sharply. That is why critical angle checks are important in beamline and mirror design.
4. What does the Bragg angle result mean?
The Bragg angle is the incidence angle that satisfies nλ = 2d sinθ. It shows when a crystal plane spacing can diffract a given x ray wavelength at a selected order.
5. Can I use noninteger diffraction order values?
Use positive integers for diffraction order. Bragg reflections are normally indexed by integer order. Fractional entries are not appropriate for this calculator mode.
6. What is zone plate focus in this tool?
It is the estimated focal length of a zone plate based on outer radius, wavelength, and diffraction order. This helps in microscopy, imaging, and compact x ray focusing setups.
7. Why is mirror footprint length useful?
Footprint length tells you how much mirror surface the beam illuminates. It helps with mirror sizing, heat load planning, beam acceptance, and clipping checks.
8. Can I save my results?
Yes. After calculation, you can export the current result table as CSV or PDF. That makes it easier to document values for reports, coursework, or beamline notes.