Wiki / Sources / Point source

Point source

Emits isotropic light — monochromatic, broadband, or the line spectrum of a gas discharge lamp — that fades over a short evanescent range unless captured by a nearby lens, objective, mirror, or fiber tip. A parabolic mirror with the source at its focus collimates it.

Open in the canvas →

A live trace, not a picture of one — but this preview is not interactive. Open it in the canvas to move things, change parameters, and save or export your own version.

In the real world

Not every source is a laser, and most of optics predates the ones that are. A point source is the opposite limit: light leaving a region small enough to treat as a point, spreading into every direction at once, with no fixed phase relationship between one direction and the next. A fluorescing molecule, the tip of a fiber, an arc between two electrodes and a pinhole in a screen all behave this way.

Two consequences follow, and between them they explain most of what such a source is like to work with. The first is that the power falls as 1/r² — spread over a sphere whose area grows with the square of the distance — so an isotropic emitter is dim at any useful range unless something gathers its light. The second is that you cannot get the brightness back. Étendue, the product of source area and solid angle, cannot be reduced by any passive optic; a lens can redirect an emitter's output but not concentrate it beyond what its own size and spread allow. This is exactly why a laser can be focused to a diffraction-limited spot and a lamp cannot, and it is a geometric limit rather than an engineering one.

Gas discharge lamps

The most useful incoherent point sources in a laboratory are gas discharge lamps, and what makes them useful is that they do not emit a continuum. Passing a current through a low-pressure gas excites its atoms, and they radiate on the discrete transitions that atom happens to have — a line spectrum, fixed by atomic structure rather than by temperature[1]. Low pressure is part of the design and not an accident: it keeps collisions rare, so the lines stay narrow instead of being pressure-broadened into a smear[2].

Those wavelengths are reproducible to a small fraction of a nanometre, which is why such lamps are also called calibration lamps: mercury's 546.074 nm green, sodium's 589 nm doublet and helium's 587.5618 nm yellow are standard lines an instrument can be checked against[2].

The line strengths are a different matter, and it is worth being blunt about it. Relative intensities depend on how the discharge is excited and drift with drive current and lamp age; they are usually not specified at all[2]. The standard tabulations carry the same warning — the RIT compilation of discharge spectra, built from Reader and Corliss's Line Spectra of the Elements, notes that its line intensities "may be quite different in the lamp you observe" and that the excitation conditions behind the tabulated values are not recorded[1]. Wavelengths are data; intensities are an illustration.

What you can rely on is the pattern. Sodium's pair of close yellow lines, neon's dense red-orange group, hydrogen's four Balmer lines and mercury's blue-green-yellow set are recognisable on sight, and that recognisability is the whole reason a spectroscopy course starts here.

E=P4πr2E = \frac{P}{4\pi r^{2}}
Irradiance from an isotropic emitter: the inverse-square law is the reason uncollected point-source light is gone within a short distance.

In OpticalSetup

The point source emits rays evenly over its emission angle — the full 360° by default — and those rays are drawn as a glow that fades within a short range unless something collects them. That fading is the model's one strong opinion, and it is there because the alternative is worse: an isotropic emitter whose rays ran forever would light up every detector on the bench at full strength, which is the opposite of how such a source behaves.

A lens, a microscope objective, a fiber tip or a mirror within range collects the light, and from that point on it is ordinary light that propagates normally. The embedded bench above shows the arrangement that makes this clearest: a parabolic mirror with the source exactly at its focus, 25 mm in front of the vertex, turning isotropic emission into a parallel beam. That is how a lamp or an arc is collimated in a real instrument, and a parabola does it without chromatic aberration — which matters here, because a lamp emits many wavelengths at once.

Lamp mode

Setting Source to Gas discharge lamp changes what the element emits and how it is drawn: a pen-ray tube rather than a star, tinted by its own lines, and emitting a fixed line spectrum instead of a wavelength you type. Eight lamps are available — mercury, sodium, cadmium, helium, hydrogen, neon, caesium and argon — each carrying the standard lines it is bought for.

The lines are carried as lines, not as a sampled curve. A grating fans exactly the wavelengths that are present and none in between, a filter passes or blocks each one on its own, and the spectrometer draws them as separate peaks. Sodium ships as its D doublet rather than as the single mean wavelength, because the pair is what makes sodium recognisable and the two do resolve.

Relative line strengths are nominal, and deliberately coarse. They are set to make each lamp look like itself, not to be photometry — for the reason given above, a real lamp's ratios are not a fixed property of the element at all.

Neither mode can interfere, and that is correct rather than a limitation. Coherent field reconstruction in this tracer is reserved for a sized, monochromatic continuous-wave laser; every other source carries power only. A lamp in an interferometer therefore produces no fringes, which is what an incoherent source does.

Simplified vs. reality

The near-field fade is a modelling device, not physics. Real isotropic light does not stop at a boundary — it keeps going, growing weaker as 1/r² — and the range here is a fixed distance rather than anything derived from the source's power or the detector's sensitivity. A collector just outside it gathers nothing when a real one would gather a little.

The source is a true point, so it has no étendue: the one property that most constrains real incoherent sources is absent, and a lens can focus this light to a spot no real lamp could reach. There is no arc length, no electrode geometry, and no angular distribution other than uniform — a real discharge is neither a point nor isotropic.

Lamp line strengths are illustrative and no absolute radiometry is attached to them, so a lamp's output is a relative weight rather than watts. Line widths are not modelled at all: each line is treated as monochromatic, with no Doppler, pressure or Stark broadening, and no self-absorption of the strong resonance lines — which is a real effect in sodium lamps in particular. Nor is there any continuum background beneath the lines, which a real discharge always has to some degree.

Related components

References

  1. M. Richmond, “Spectra of Gas Discharges,” RIT PHYS 230 — simulated discharge spectra from Reader & Corliss, “Line Spectra of the Elements” (CRC Handbook / NSRDS-NBS 68), with the author's own warning that tabulated line intensities need not match the lamp in front of you
  2. R. Paschotta, “Spectral Lamps,” RP Photonics Encyclopedia; doi:10.61835/zgq

Further reading