Enter Optical and Slab Parameters
Use percentages for transmission and reflectance. Choose the solving mode that matches your known inputs.
Sample Engineering Inputs and Outputs
| Sample | Wavelength (nm) | Thickness | Reflectance (%) | Transmission (%) | Estimated α (cm^-1) |
|---|---|---|---|---|---|
| Borosilicate slab | 550 | 5 mm | 4 | 89 | 0.071 |
| Polymer optical sheet | 850 | 2 mm | 3 | 65 | 1.845 |
| Semiconductor slab | 1450 | 500 um | 18 | 12 | 34.46 |
Equations Behind the Calculator
Beer–Lambert with surface loss correction:
T = (1 - R)² × e-αd
Where T is transmission, R is reflectance, α is absorption coefficient, and d is slab thickness.
Solve for absorption coefficient:
α = -ln(T / (1 - R)²) / d
Use this when transmission and thickness are known.
Solve for slab thickness:
d = -ln(T / (1 - R)²) / α
Use this when transmission and absorption coefficient are known.
Absorbance relation:
A = log₁₀(I₀ / Iₜ)
α = 2.303 × A / d
This converts absorbance into absorption coefficient when thickness is available.
Penetration depth:
δ = 1 / α
This indicates the thickness at which intensity falls by roughly a factor of e.
Usage Steps
- Select the solving mode that matches your known quantities.
- Enter transmission and reflectance as percentages, not decimals.
- Choose the thickness unit and absorption coefficient unit that match your data.
- Add wavelength and material name if you want a clearer report.
- Submit the form to show the result block above the form.
- Review the chart, notes, and normalized transmission for consistency.
- Use the CSV button for spreadsheets and the PDF button for shareable reports.
Answers on PbSe Size Confinement
The effect of size confinement on the optical absorption coefficient of PbSe
Strong size confinement in PbSe nanocrystals increases the effective bandgap, blue-shifts the absorption edge, and can reshape absorption magnitude through altered density of states, oscillator strength, and surface effects.
Why confinement changes PbSe absorption
When PbSe particle size approaches the exciton Bohr radius, electronic levels become quantized. Optical transitions then move to higher energies, so absorption starts at shorter wavelengths and often shows sharper spectral features.
Frequently Asked Questions
1) What does this calculator solve?
It solves absorption coefficient, slab thickness, transmission, absorbance, and penetration depth using Beer–Lambert relations with optional reflectance correction.
2) Which equation is the main model?
The main model is T = (1 − R)²e−αd. It combines material absorption with interface reflection losses for a simple passive slab.
3) When should reflectance be included?
Include reflectance when surface losses are not negligible, especially for polished slabs, semiconductors, and higher-index materials.
4) Can I estimate reflectance from refractive index?
Yes. This file can estimate normal-incidence reflectance from refractive index when reflectance is left blank, but the approximation is simplest for non-scattering surfaces.
5) What units are supported?
Thickness supports nm, um, mm, cm, and m. Absorption coefficient supports cm^-1, m^-1, and mm^-1.
6) What is penetration depth?
Penetration depth is 1/α. It estimates how far light travels before intensity drops by about 63 percent in the absorbing medium.
7) What is the effect of size confinement on the optical absorption coefficient of PbSe?
Strong size confinement in PbSe raises the effective bandgap, blue-shifts the absorption edge, and modifies absorption strength through quantized states and surface effects.
8) Why does PbSe quantum confinement shift the absorption onset?
When crystal size nears the exciton Bohr radius, electronic states quantize. Allowed transitions move to higher energies, causing shorter-wavelength absorption onset.