---
title: "Blackbody Radiation Observatory Interactive Lab | Sandbox Physics"
description: "Can one temperature and one emissivity explain the measured spectrum? In this simulated measurement, yes."
canonical_url: "https://sandboxphysics.com/labs/blackbody-radiation/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/blackbody-radiation/"
last_modified: "2026-10-30"
---

Quantum evidence / Thermal radiation

# Blackbody Radiation Observatory

**Can one temperature and one emissivity explain the measured spectrum?** In this simulated measurement, yes. Fit Planck's law with one temperature and one emissivity to the power measured in each wavelength band, and it reproduces the whole spectrum. Classical equipartition cannot: at best it follows the long-wave end, and it blows up toward short wavelengths.

Pass thermal radiation through a scanning monochromator and take an open and a dark reading at each wavelength. Fit the temperature and emissivity to the spectrum you collect, and see where classical equipartition fails.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The source is gray and isothermal, and the detector is an ideal power meter. The simulated readings include a finite spectral bandwidth and independent Gaussian read noise. This is a teaching instrument; it does not use historical data and is not a calibrated reproduction of a NIST facility.

Schematic cutaway with the aperture and slit enlarged. Amber paths also stand for invisible infrared. Drag to orbit.

Acquire readings, not just a curve

## Build the spectrum, one reading at a time.

Each point records an open exposure and an independent shuttered dark exposure. Playback is accelerated; integration time controls noise.

Ready. Predict the peak, then scan.

Recorded points

$0$

Wavelength peak · model

$0$

Probe power · model

$0$

Total exitance · model

$0$

Spectrum on a log wavelength axis

### Does the shape agree?

$\lambda/\mathrm{\mu m}$ · $\overline L_\lambda/(\mathrm{W\,m^{-2}\,sr^{-1}\,\mu m^{-1}})$

Teal: Planck source reference through the passband. Gold: dark-subtracted records, one standard uncertainty. Purple dashes: selected fit. Gray: saved run. Negative records are kept.

Click or drag the spectrum to move the probe; the wavelength slider also supports keyboard input. The vertical scale follows the curves.

Inference from the records only

Candidate law

Fitted temperature

$\text{—}$

Fitted emissivity / classical product

$\text{—}$

Reduced chi-squared

$\text{—}$

$r_i=(P_i^{\mathrm{net}}-P_i^{\mathrm{fit}})/u_i$

Fits integrate the same passband. Planck and Wien fit temperature and gray emissivity; the classical fit identifies only their product. No confidence interval or discovery significance is claimed.

### Keep a comparison

Save one complete or partial run with its settings and raw readings.

| # | $\lambda/\mathrm{\mu m}$ | Open $/\mathrm{nW}$ | Dark $/\mathrm{nW}$ | Net $/\mathrm{nW}$ |
| --- | --- | --- | --- | --- |

Latest six readings shown; CSV includes every reading, uncertainty, source setting, passband and seed. Save and restore work in this page session.

Scientific scope & primary sources

Uniform gray radiance; zero incident background, ideal shutter and known constant throughput. No atmospheric bands, stray light, wavelength-dependent emissivity, photon bunching, shot noise, saturation or thermal transients. Independent additive Gaussian read noise is the only detector noise. The 0.5–12 micrometre range is an ideal broadband instrument, not the stated range of FASCAL. Cavity glow and moving markers are presentation, not calibrated color or photon trajectories.

The source uses Planck’s law. Recovering it from these synthetic readings tests the simulator; it does not provide independent evidence for quantization. Absolute detector response is assumed known independently. A response calibrated by assuming Planck’s law cannot independently test that same law.

[NIST · FASCAL](https://www.nist.gov/laboratories/tools-instruments/facility-spectroradiometric-calibrations-fascal) [NIST · Planck and radiometry](https://nvlpubs.nist.gov/nistpubs/sp958-lide/html/007-009.html) [CODATA · constants](https://physics.nist.gov/cuu/Constants/Table/allascii.txt)

[Read the quantum evidence collection](https://sandboxphysics.com/stories/quantum-evidence/)

Physics tutorial

## Testing a radiation law with one spectrum

**Background** Pass thermal radiation through a scanning monochromator and take an open and a dark reading at each wavelength. Fit the temperature and emissivity to the spectrum you collect, and see where classical equipartition fails.

**Why it matters** Brightness alone is not enough; the evidence is how the power changes with wavelength.

Start with the essentials

- **Focus question**: Which parts of the spectrum distinguish the three laws?
- **One-sentence intuition**: Fit each candidate law to the same measured powers through the same passband. A law that works well at short wavelengths can still fail at long ones.

### Core mathematical model

#### Radiance per wavelength

$$
B_\lambda(T)=\frac{2hc^2}{\lambda^5}\frac{1}{\exp(hc/\lambda k_{\mathrm B}T)-1}
$$

Wavelength is the vacuum wavelength in metres and temperature is in kelvin. Radiance is power per unit area, solid angle and wavelength, which is different from radiant exitance.

#### What reaches the detector

$$
P_i=G\varepsilon\int_{\lambda_i-\Delta\lambda_i/2}^{\lambda_i+\Delta\lambda_i/2}B_\lambda(T)\,\mathrm d\lambda,\quad G=10^{-10}\,\mathrm{m^2\,sr}
$$

The passband is a top hat, and its throughput is constant and known independently. The source fills the field the instrument accepts, and the detector measures the power integrated over the band.

#### Two useful limits

$$
B_\lambda^{\mathrm W}=\frac{2hc^2}{\lambda^5}e^{-hc/\lambda k_{\mathrm B}T},\qquad B_\lambda^{\mathrm{RJ}}=\frac{2ck_{\mathrm B}T}{\lambda^4}
$$

Wien describes the short-wave limit. Rayleigh–Jeans describes the long-wave limit, where temperature and gray emissivity enter only as their product.

#### Peak and total power are different tests

$$
\lambda_{\mathrm{peak}}T=2897.771955\,\mathrm{\mu m\,K},\qquad M=\varepsilon\sigma T^4
$$

The peak is the peak of radiance per wavelength. Total exitance adds up all wavelengths and all directions in the outward hemisphere. Both values shown here come straight from the model; they are not estimated from the finite scan.

### Common difficulties

#### A simulation is not an independent discovery

**Typical misconception** A good Planck fit proves that the real world follows this law.

**Better mental model** These observations are generated from Planck radiation. Real evidence needs an independently calibrated instrument response, historical or new observations, an account of systematic uncertainties and a comparison with competing explanations.

### Run the experiment

1. 01

   #### Predict the peak

   Scan the default cavity, save the sample, then choose the hotter source and scan again.

   **What to observe:** The peak moves to shorter wavelengths and the spectrum gets brighter. A gray emissivity changes the height of the curve but does not move the ideal peak.

2. 02

   #### Test an approximation

   Compare the short-wave preset with the full scan. Switch the fitted law and look at the standardized residuals.

   **What to observe:** Every fit uses only the recorded net power. With emissivity unknown, the classical law cannot pin down a unique temperature, because only their product enters.

3. 03

   #### Test the instrument settings

   Widen the passband, shorten the integration time and export the open and dark records. Then restore a saved run.

   **What to observe:** The fit integrates over the finite passband. A shorter integration time raises the noise, and subtracting the dark reading from the open one adds their variances. Net powers that noise pushes below zero are kept.

Physical conclusion

The simulation generates Planck radiation, so fitting Planck's law back checks the simulated measurement chain. It does not independently establish the historical law.

## Related experiments and articles

Quantum evidence · Reading path

### Laws and the formation of quantum mechanics

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Blackbody radiation: a whole curve, not one quantum**](https://sandboxphysics.com/stories/quantum-evidence/blackbody-spectrum-planck-wien/)

Fluctuational electrodynamics · Reading path

### From thermal emission to heat and force across a nanometre gap

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why hot surfaces glow, and why a good mirror glows weakly**](https://sandboxphysics.com/stories/fluctuational-electrodynamics/thermal-emission-and-kirchhoff/)
2. [Lab **Near-Field Thermal Radiation: Probe Above Hot SiC** See the emission dip of SiC from far away](https://sandboxphysics.com/labs/thermal-near-field-probe/)

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)