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An excitation spectrum records a sample's fluorescence signal as the excitation wavelength is varied while the observation band is held fixed. It asks which incident wavelengths efficiently produce the selected emission. An emission spectrum instead varies the observed emission wavelength for a fixed excitation setting.

A fluorometer implements the scan with its excitation monochromator while keeping the emission selection fixed. For example, observing near $520\mathrm{nm}$ while scanning excitation from $400$ to $490\mathrm{nm}$ defines an illustrative excitation scan; it is not a measurement of a named substance. Finite band widths and the instrument's wavelength-dependent response are part of the measurement.^[ref][ref]

For a homogeneous sample under a simple photon-balance model, writeHere $q$ is the incident photon rate, $A$ the absorbance, $\Phi$ the fluorescence quantum yield, and $K$ a constant detection fraction including the selected emission band. This model assumes that emitted light is not appreciably reabsorbed and that the collection and emission-band fractions remain constant.

When $A$ is small, $1-10^{-A}\simeq (\ln 10)A$. After correcting for the incident photon rate, the excitation shape then follows the absorption spectrum if $\Phi$ and the other stated factors stay constant. For $A=0.01$ and $0.02$ at two settings, the predicted corrected-signal ratio is approximately two; the exact absorbed-fraction ratio is about $1.98$. Unequal incident photon rates would change the raw ratio even for the same sample.

An excitation spectrum is consequently not automatically an absorption spectrum. Multiple emitters, wavelength-dependent yield and an inner filter effect can change the correspondence. JASCO's dilute-versus-concentrated comparison, monitored at $450\mathrm{nm}$ emission, illustrates concentration-dependent distortion of an excitation scan.^[ref]

Overlap of a gas absorption spectrum with existing atmospheric absorption changes its incremental radiative effect. A strong band in an already opaque spectral interval can contribute less additional outgoing-flux reduction than a weaker band in a window. Pressure broadening, altitude, temperature and the source spectrum also matter.

For the absorption spectrum, pass a scanned monochromatic beam through the solution and a matched solvent reference. Record the incident and transmitted intensities and calculate the absorbance $A(\lambda )={\log }_{10}[I_0(\lambda )/I(\lambda )]$, using an appropriate blank and concentration to avoid saturation.

For the fluorescence emission spectrum, excite at a fixed wavelength within an absorption band, collect emission away from the incident beam, commonly at $90^{\circ }$, and scan an emission monochromator. Correct the detected signal for wavelength-dependent detector sensitivity, subtract solvent/background light and exclude scattered excitation light. The two plotted vertical scales have been independently normalized; their equal peak heights do not imply equal absorption and emission rates or unit fluorescence quantum yield.

First record the position, extent, colour and underlying material of the stain. Keep a portion untouched, take a small scraping or cutting for examination, and test an unstained portion of the same material alongside it. The comparison is important: a coloured fabric, iron oxide or a vegetable colouring substance may resemble dried blood, and the material itself can interfere with a chemical test. Brown colour alone proves nothing.

For an examination practicable in 1867, use complementary observations:

These observations should agree before the examiner expresses a positive conclusion. Failure to recover intact red blood cells does not exclude an old bloodstain; conversely, a colour reaction without suitable controls is weak evidence. A defensible period report would distinguish “blood identified, consistent with mammalian origin” from “human blood proved.” The second conclusion does not follow from the first.

For comparison, later precipitin tests use antibodies against human proteins to investigate species of origin. Modern DNA profiling can investigate the donor, subject to preservation and contamination limits. These are later developments, not procedures to attribute to an Oxford candidate in 1867.^[ref]

With the graphene lattice-vector length $a=0.246\mathrm{nm}$, the carbon nanotube chiral vector is ${\mathbf{C}}_h=n{\mathbf{a}}_1+m{\mathbf{a}}_2$. The vectors meet at $60^{\circ }$, givingHere $C$ is circumference, $d$ diameter, and the carbon nanotube chiral angle $\theta$ is measured from the zigzag direction. Nanotube zone folding gives a nominal metallic tube when $n-m\equiv 0(\mathrm{mod}3)$ and a semiconducting tube otherwise. Evaluating all the supplied indices gives the following derived results:All eleven listed tubes are semiconducting in the zone-folding classification. Curvature can open small gaps in some nominally metallic non-armchair tubes, but none of these indices falls in that nominal metallic class.

Diameter gives a useful inverse-size trend in transition energies, and the full chiral indices constrain the electronic band structure much more strongly. They do not by themselves give the perceived solution colour through a simple geometrical rule: one needs the visible absorption spectrum, transition strengths and widths, exciton/environment shifts, concentration, optical path and illumination. The observed transmitted colour is complementary to the absorbed spectrum, not a direct label for the band gap. Structure-assigned excitation–emission measurements provide an experimental connection between chiral structure and optical transitions.^[ref]

A secondary inner filter effect occurs when emitted fluorescence is absorbed within the sample before reaching the detector. The absorption changes the collected signal and can distort its emission spectrum, especially when absorption differs strongly between emission wavelengths. It concerns the emitted-light path, whereas a primary inner filter effect concerns the excitation path.^[ref]

For a small emitting region followed by a purely attenuating detection path, let $A_{\mathrm{em}}(\lambda )$ be the path absorbance at emission wavelength $\lambda$. The Beer-Lambert law gives the simple modelThe path geometry is part of this statement; a whole-cell absorbance must be scaled to the path actually traversed.

For a synthetic two-band example, suppose equal intrinsic signals of $100$ units face path absorbances $0.1$ and $0.5$. The collected signals becomeTheir ratio is now $10^{-0.4}\simeq 0.398$, although the intrinsic ratio was one. A distorted band ratio can thus arise without a change in the relative emission initially produced.

Within this attenuation-only model, multiplying each observed band by $10^{A_{\mathrm{em}}(\lambda )}$ recovers its intrinsic value. Real collection samples an extended volume, and scattering or absorption followed by re-emission can require a richer model. An absorbance-based correction is consequently meaningful only with its geometry and assumptions stated.^[ref]

A practical comparison measures an absorption spectrum along with fluorescence and repeats the measurement with a shorter detection path or suitable dilution. Record raw intensities as well as normalized spectra: normalizing peaks can hide a large loss of detected light. A fluorescence blank removes additive background under matched conditions, but does not by itself undo this wavelength-dependent attenuation.

A single-line greenhouse deficit measures the reduction of outgoing thermal radiative flux by one isolated absorption line. Consider a plane-parallel atmosphere in local thermodynamic equilibrium, without scattering, above a blackbody surface. Let pressure $p$ increase from zero at the top to $p_s$ at the surface, and let the surface share the adjacent gas temperature $T_s$.

To specify the angular approximation, use one effective upward direction cosine $0<{\mu }_d\le 1$ and a flux closure $F_{\nu }=\pi I_{\nu }$. Define the corresponding transmission ${\mathfrak{T}}_{\nu }(p)=\exp [-{\tau }_{\nu }(p)/{\mu }_d]$. Integration by parts of the formal radiative transfer solution givesFor a sufficiently narrow absorption line centred at frequency ${\nu }_0$, replace the Planck function and its temperature derivative across the line by their values at ${\nu }_0$. With the line equivalent widththe outgoing radiative flux becomesIf temperature increases downward, $D\ge 0$. An atmospheric thermal inversion can invalidate that sign argument; absorption alone does not guarantee a positive deficit for every imposed thermal profile.

For constant absorber mass fraction $q$, constant gravity $g$ and an opacity ${\kappa }_{\nu }=S{\varphi }_{\nu }$ per absorber mass, assume $\int {\varphi }_{\nu }d\nu =1$ and constant integrated strength $S$. Then ${\tau }_{\nu }=qS{\varphi }_{\nu }p/g$. In the optically thin limit for the specified direction,This leading term is independent of the normalized shape of the absorption spectrum. The angular closure and abundance convention must accompany the coefficient; a full angular integration uses its own flux-weighted transmission.

A spectroscope makes an optical spectrum observable, commonly by passing light from an entrance slit through a collimator and an optical prism or diffraction grating. An eyepiece permits direct inspection of separated spectral lines or bands, while a recording detector makes the instrument a spectrograph.

An emission lamp gives bright spectral lines; placing an absorbing sample in front of a continuous source can produce an absorption spectrum. Slit width affects both received radiant power and the ability to distinguish neighboring features. A visible dark band must be checked against the source spectrum and instrument response before being assigned to sample absorption.