Spectroscopy

What can happen when EM radiation interacts with matter?

3 main outcomes: (1) ABSORPTION (energy taken up, molecule goes to an excited state), (2) EMISSION (energy released as light), (3) SCATTERING (light redirected, e.g. Rayleigh/Raman). Other effects: transmission, reflection/refraction/diffraction, polarization, photoelectric effect, nonlinear effects, surface plasmon resonance.

[Light] What is wave-particle duality of light?

Light is BOTH a wave (amplitude A, wavelength λ, frequency ν, phase φ; shows interference + diffraction) AND a stream of quantised particles = photons. Speed in vacuum c = 299,792,458 m/s ≈ 0.3 m/ns, and c = λν.

[Planck relation] Energy of one photon?

E = hν = hc/λ (h = Planck's constant = 6.626×10⁻³⁴ J·s). Higher frequency / shorter wavelength = MORE energy per photon.

[Wavenumber] What is the wavenumber ν̃ and where is it used?

ν̃ = 1/λ (units cm⁻¹). It is proportional to energy. Used in IR spectroscopy (e.g. 700-4,000 cm⁻¹).

[Unit conversions] How do you convert photon energy from J to eV and to kJ/mol?

J per photon ÷ 1.6×10⁻¹⁹ J/eV = eV. J per photon × Avogadro's number (6×10²³) = J/mol (then ÷1000 for kJ/mol).

[Worked example] A 600 nm photon: ν, E (J), E (eV), E (kJ/mol), ν̃?

ν = c/λ = 3×10⁸ / 6×10⁻⁷ = 5×10¹⁴ Hz. E = hν = 6.63×10⁻³⁴ × 5×10¹⁴ = 3.3×10⁻¹⁹ J = 2 eV ≈ 200 kJ/mol. ν̃ = 1/λ = 1.67×10⁴ cm⁻¹.

[EM spectrum] Order of the EM spectrum from SHORT to LONG wavelength?

Gamma (~10⁻¹² m) → X-rays (~10⁻¹⁰) → Ultraviolet (~10⁻⁸) → Visible (~400-750 nm) → Infrared (~10⁻⁶ to 10⁻⁴) → Microwaves (~10⁻²) → Radiowaves (10⁰ to 10⁶ m). Shorter λ = higher energy.

[UV/Vis ranges] Wavelength ranges: VUV, UVC, UVB, UVA, visible?

VUV ~100-200 nm; UVC ~200-280 nm (ozone absorbs ~200-290 nm); UVB ~280-315 nm; UVA ~315-400 nm; Visible ~400-750 nm (slide: ~390-780). Bees can see ~300-650 nm (into the UV). ★ exact UV band edges are standard values.

Are electrons + neutrons EM radiation?

NO, but they have a wavelength that is inversely related to their momentum (de Broglie): λ = h/mv. (Faster/heavier particle → shorter λ.)

[Energy levels] What is the Boltzmann law?

Energy is quantised, and molecules distribute over the levels as n_u/n_g = exp(−ΔE/RT) (n_u = excited, n_g = ground; R gas constant; ΔE energy gap; T temperature). Bigger gap or lower T → fewer molecules in the excited state.

[NMR energy levels] How are energy levels created in NMR?

A magnetic field B₀ splits the nuclear-spin energy states into discrete levels. B₀ = 0: no splitting; B₀ > 0: levels split (this is an INDUCED energy separation).

[Energy scale] Order the transition types from HIGHEST to LOWEST energy

Inner-electron transitions (X-rays) > bonding/outer-electron transitions (UV/Vis, ~10⁵ J/mol) > molecular vibrations (IR, ~10⁴ J/mol) > electron spin + molecular rotations (microwaves) > nuclear spin flips (radiowaves, ~10⁻³ J/mol).

[Techniques map] Which technique goes with which region?

X-rays: XAS/EXAFS (inner electrons). UV/Vis region: UV/Vis absorption, fluorescence, (resonance) Raman (outer electrons). IR: IR/Raman (vibrations). Microwaves: EPR (electron spin). Radiowaves: NMR (nuclear spin).

[Population: NMR vs UV/Vis] What are n_u/n_g for NMR vs UV/Vis, and what does it mean?

NMR: ΔE ~10⁻³ J/mol → n_u/n_g ≈ 0.99999 (levels almost equally populated). UV/Vis: ΔE ~10⁵ J/mol → n_u/n_g ~10⁻²¹ (essentially everything in the ground state). Greater population difference = greater sensitivity (less sample / lower concentration needed). So UV/Vis is intrinsically more sensitive than NMR.

Why do we NEED a population difference to see a signal?

Applied EM radiation stimulates absorption and emission EQUALLY. Net signal only appears if more molecules are in the ground state than the excited state (n_g − n_e). Sensitivity (S/N) depends on this population difference.

[Relaxation] How does a system return to equilibrium after absorbing, and what does the spectrum look like?

By RELAXATION (e.g. emission/non-radiative decay). Absorption between quantised levels gives discrete resonances (peaks/lines) in a plot of absorbed energy vs. λ, ν or ν̃. Many spectra show broad peaks = superposition of unresolved lines.

[Linewidth] What determines peak linewidth (Δν) and why does it matter?

Δν depends on the LIFETIME (τ) of the excited state (Δν ~ 1/τ). FAST decay → position uncertain → BROAD line. SLOW decay (e.g. NMR) → SHARP lines. Linewidth sets spectral resolution, so it affects the information content of the spectrum.

State the Franck-Condon principle

Electronic transitions occur much faster (∼10^-15s) than nuclear vibrations. Therefore, nuclei remain essentially fixed during the transition; electronic energy changes while internuclear distance stays approximately constant, so transition is drawn vertically.

[Morse curves] What do the energy (Morse) curves of ground and excited states show?

Energy vs. bond length / reaction coordinate r, each electronic state with its own vibrational levels. Usually r_g (ground) < r_e (excited): the excited-state minimum is at a longer bond length. Curve shapes are influenced by the environment (solvent, pH, etc.).

Name the processes on a Jablonski diagram

Absorption → S0→S1/S2

Vibrational relaxation → loses vibrational energy within same electronic state

Internal conversion (IC) → non-radiative transition between electronic states of the same spin (e.g. S2→S1)

Fluorescence → radiative transition S1→S0

Intersystem crossing (ISC) → non-radiative transition between states of different spin (e.g. S1→T1)

Phosphorescence → radiative transition T1​→S0

[Stokes shift] Why is fluorescence emitted at a LONGER wavelength than the absorbed light?

Before emitting, the molecule loses some energy by vibrational relaxation / heat, so the emitted photon has less energy (longer λ) than the absorbed one.

[Atomic spectra] Atomic EMISSION vs ABSORPTION spectra?

Atoms have discrete energy levels. EMISSION: bright lines at specific wavelengths (excited atoms drop down). ABSORPTION: dark lines on a continuous background at the same wavelengths. Line positions = fingerprint of the element.

[Stimulated emission] What is stimulated emission?

A photon with hν = ΔE hits an excited molecule and triggers it to emit a second, identical photon (same frequency, phase, direction). Basis of the LASER. (Slide title typo: 'Simulated' emission.)

What is resonance in spectroscopy?

Maximum effect when the applied photon energy hν matches the energy-level separation ΔE.

Why do selection rules exist?

The E-field of the EM radiation only interacts effectively if there is a CHARGE DISPLACEMENT (change in dipole) when going between states. No charge displacement → transition 'forbidden' (weak or absent).

[Selection rules: UV/Vis] Which electronic transitions are allowed/forbidden?

1s→2s is FORBIDDEN (no charge displacement, Δl = 0). s→p is ALLOWED (Δl = ±1, charge moves) and π→π* is ALLOWED.

Examples of IR-forbidden vs IR-allowed?

N≡N symmetric stretch = no IR (no dipole change). O=C=O ASYMMETRIC stretch = IR (dipole changes). Rule of thumb: IR needs a change in DIPOLE moment; Raman needs a change in POLARISABILITY.

[Transition dipole moment] What is μ (transition dipole moment)?

A vector that quantifies the charge displacement during a g→e transition. Bigger charge displacement → bigger μ → more probable transition → stronger absorbance. Its DIRECTION depends on chemical structure (e.g. of a chromophore).

[Angle dependence] How does excitation depend on the polarisation of light?

Excitation is angle-dependent because μ has a direction. If the polarisation of the excitation is at 90° to μ → NO induced transition (best when parallel).

Which part of EM radiation drives most transitions?

The ELECTRIC (E) component → linear charge displacement. Interaction with both E and M components → circular charge displacement = optical activity (see CD/ORD).

An electric field component + magnetic field component. The electric field describes how photons travel through space; it is drawn as a wave, polarised when we select a single plane.

[UV/Vis] Range and what is a chromophore?

UV/Vis spectroscopy: ~200-750 nm

CHROMOPHORE = molecule/group that absorbs in this range. Examples: aromatic amino acids, nucleotide bases, chlorophyll, haem, some transition metals.

[UV/Vis] Advantages / uses?

Concentration measurement (Beer's law); sensitive (µM concentrations); inexpensive; simple; fast.

[Beer-Lambert law] Formula and symbols?

A = log₁₀(I₀/I_t) = ε·c·l. I₀ = incident intensity, I_t = transmitted intensity, ε = molar absorptivity (M⁻¹cm⁻¹), c = concentration (M), l = path length (cm). A is linear in c (for dilute solutions). ★ A = 1 means 10% of light transmitted.

[Beer-Lambert calculation] ε = 5,500 M⁻¹cm⁻¹, A = 0.55, l = 1 cm. Concentration?

c = A/(ε·l) = 0.55 / (5,500 × 1) = 1×10⁻⁴ M = 100 µM.

[Dispersing light] Diffraction grating vs prism?

Both split light into its wavelengths (used in monochromators). Grating = diffraction/interference; prism = refraction.

A grating gives ~linear dispersion; a prism's dispersion is non-linear.

[Pigment spectra] Chlorophyll a and β-carotene absorption?

Chlorophyll a absorbs mainly blue (~430 nm) and red (~660 nm) and reflects green. β-carotene absorbs blue-green (~450-500 nm). Chlorophyll a and b differ slightly in structure, so their spectra differ: absorption spectra can be TUNED by small structural changes; peak positions from the graph

[Eye] What happens to retinal when it absorbs light?

retinal absorbs a photon → gains energy → retinal changes shape → rhodopsin activated → visual nerve signal to the brain

[Colour vision] How do we see different colours if the chromophore is always retinal?

Three rhodopsin homologues (cone pigments) give three different absorption spectra. Amino-acid substitutions in the PROTEIN change the absorbance of the same retinal chromophore. Colour blindness = altered/missing cone pigment ★ (Ishihara test).

[Protein UV] Which residues absorb in proteins and at what wavelengths?

Peptide bond ~200 nm. Above 230 nm: Trp (λmax 280 nm, ε ≈ 5,500 M⁻¹cm⁻¹) > Tyr (274 nm, ε ≈ 1,490) ≫ Phe (257 nm, weak, ε ≈ 200) plus cystine S-S (ε ≈ 125). Trp + Tyr dominate the A280.

[Protein concentration] How to calculate protein concentration from A280?

ε_prot = n_Trp·ε_Trp + n_Tyr·ε_Tyr + n_cystine·ε_cystine, with ε_Trp = 5,500, ε_Tyr = 1,490, ε_SS = 125 M⁻¹cm⁻¹. Then c = A₂₈₀ / (ε_prot · l). (Needs the protein sequence: counts of Trp, Tyr, cystine.)

[Nucleic acids UV] Where do nucleic acids absorb and how is concentration found?

230-290 nm, mainly from the BASES, λmax ≈ 258-260 nm (DNA 258, RNA 258). Use A260. Slide values: 0.020 (dsDNA) and 0.027 (ssDNA and RNA) in mL·µg⁻¹·cm⁻¹. ⚠ Slide writes the units as µg·mL⁻¹·cm⁻¹ (wrong way round). Rule of thumb: A260 = 1 ≈ 50 µg/mL dsDNA (=1/0.020), ~33 µg/mL ssDNA, ~40 µg/mL RNA ★.

[ssDNA vs dsDNA] Which absorbs more at 260 nm?

Single-stranded DNA absorbs MORE than double-stranded (slide figure: ss above ds). Base stacking in dsDNA lowers absorbance (hypochromism) ★, so melting/denaturing raises A260.

[IR] What does IR detect and in what range?

Molecular VIBRATIONS. Observable range ν̃ = 700-4,000 cm⁻¹

What is IR sensitive to?

H-bonding, secondary structure, H/D exchange, and ionisation states.

2 main limitations of IR?

(1) Large number of peaks: 3n−6 vibrations for a non-linear n-atom molecule (3n−5 if linear) → problems with resolution and with assigning peaks to specific vibrations. (2) Strong absorption by solvents (water!) and sample cells.

[Dispersive IR instrument] Components of the classic IR spectrometer?

Source: heated metal carbide (many wavelengths). Monochromator: grating or prism (one wavelength at a time). Sample cell: must be non-absorbing, e.g. CaF₂, LiF, NaCl. Detector: heat detector. Now REPLACED by FTIR and ATR-FTIR (much faster and more sensitive).

How is vibration frequency modelled?

Bonded atoms = springs doing Simple Harmonic Motion (SHM): ν_vib = (1/2π)·√(k/M). k = force constant (bond stiffness), M = mass (reduced mass ★). Stiffer bond or lighter atoms → HIGHER frequency. Real bonds are anharmonic (Morse curve). ★ Link: H/D exchange shifts peaks because D is heavier → lower frequency.

[Amide bands] What are amide I and amide II?

Characteristic IR bands of proteins from vibrations of the planar PEPTIDE group. Their positions are sensitive to secondary structure (α-helix vs β-sheet). Amide I ≈ 1650 cm⁻¹ (mostly C=O stretch); amide II ≈ 1550 cm⁻¹ (N-H bend + C-N stretch).

[Bacteriorhodopsin] How was IR difference spectroscopy used on bR?

bR can be trapped in the 412 nm (A) or 570 nm (B) state of its UV/Vis photocycle and an IR spectrum recorded for each. The IR DIFFERENCE spectrum (B−A) shows only the vibrations that changed → tells us about vibrations around the chromophore. ★ difference spectra cancel the huge unchanged background.

[Raman principle] What is Raman scattering?

measures inelastic scattering of laser light; during scattering, energy can be exchanged between photon + molecular vibrational modes, causing scattered light to have different frequency from incident light; frequency shifts provide info about molecular vibrations; vibration is Raman-active when it produces a change in the molecule's polarisability.

[Raman lines] Rayleigh vs Stokes vs anti-Stokes?

RAYLEIGH: same frequency as laser (no change in vibrational state). STOKES: scattered light at LOWER frequency (molecule ends in a higher vibrational level). ANTI-STOKES: scattered light at HIGHER frequency (molecule started in an excited vibrational level). Mnemonic: Stokes = light 'Sinks', anti-Stokes = light goes up.

[Raman intensity] Order of scattering intensities?

Rayleigh (static) ≫ Stokes > anti-Stokes. Rayleigh is ~10⁶ stronger than Raman. Anti-Stokes is weaker because few molecules start in an excited vibrational level (Boltzmann) ★.

Raman is weak: how is sensitivity boosted?

Resonance Raman: tune the laser to an electronic transition to enhance a chromophore’s vibrations;

SERS: laser → metal creates strong local field → molecule's electron cloud is distorted more strongly → stronger Raman scattering → metal also enhances the emitted Raman field → much stronger detected signal.

What is optical activity?

chromophore is optically active if it rotates the plane of polarisation of light; caused by intrinsic chirality ('handedness') or chirality induced by local structure, e.g. a helix.

Difference between ORD and CD?

ORD = differential ROTATION of left (L) vs right (R) circularly polarised light; not very sensitive for biological use. CD = differential ABSORPTION of L vs R. CD and ORD are equivalent, but CD is more common in biology.

How is Circular Dichroism used for protein structure?

measures difference in absorption of left- + right-circularly polarised light; resulting spectrum provides info about protein secondary structure + conformational changes; compare far-UV CD curve with curves generated from reference spectra (α-helix, β-sheet, random coil) → estimate the secondary-structure content; α-helix shows 2 minima

[CD: DNA] What did CD show for DNA?

CD spectra are sensitive to DNA conformation (A-form, B-form, bent). Study: the DNA sequence that binds TFIIIA gave a spectrum different from standard B-DNA → it is already distorted BEFORE the protein binds.

[XAS] How does X-ray absorption work (XAS)?

High-energy X-rays are absorbed by INNER core electrons: an electron is ejected from the K shell. K hole is refilled by an outer electron → X-ray fluorescence (XRF), characteristic of the atom type;useful for metalloproteins

[XAS regions] The two regions of an XAS spectrum?

(i) EDGE: sharp rise in absorption when the X-ray energy reaches the core-electron transition (element-specific; oxidation state ★). (ii) EXAFS: wiggles above the edge from INTERFERENCE between the outgoing ejected electron wave and waves BACKSCATTERED from neighbouring atoms → info on neighbours (distance, number, type ★).

[X-ray crystallography] Steps from crystal to structure?

Crystal → X-rays → diffraction pattern → phases → electron density map → fitting an atomic model → refinement (loop back to phases); Phase problem: detectors record intensities but not phases.

What is Auger electron spectroscopy?

A core electron is ejected (by electron/X-ray collision), an outer electron falls into the hole, and instead of emitting an X-ray the energy is passed to ANOTHER electron, which is ejected: the Auger electron, with kinetic energy characteristic of the atom. Competes with X-ray fluorescence. ★ surface-sensitive.

[Check] Why can UV/Vis detect µM concentrations while NMR needs far more sample?

Sensitivity depends on the population difference (n_g − n_e). UV/Vis: ΔE ~10⁵ J/mol → almost all molecules in ground state (big difference). NMR: ΔE ~10⁻³ J/mol → populations nearly equal (tiny difference) → weak signal.

[Check] Why is the electronic transition drawn vertical?

Franck-Condon: electronic transition (~10⁻¹⁵ s) is much faster than nuclear motion, so r does not change during absorption.

[Check] Why do the same chromophore's spectra differ in a protein vs in solvent?

Environment changes the energy curves (solvent, pH) and neighbours/protein residues perturb μ and ΔE (e.g. rhodopsin opsins tune retinal; BChl special pair vs BChl in ether).

[Check] A protein has no Trp or Tyr. Is A280 a good way to measure concentration?

No: A280 is dominated by Trp, Tyr (and a little cystine). With none, A280 is tiny/unreliable. Use the peptide bond near ~200 nm or another assay ★.

[Check] Protein in water: IR or Raman, and why?

Raman is easier: water is a weak Raman scatterer but absorbs IR strongly (IR limitation). IR is still possible with thin cells, ATR-FTIR or D₂O

[Check] Why are anti-Stokes lines weaker than Stokes lines?

Anti-Stokes needs the molecule to START in an excited vibrational level; by Boltzmann few molecules are there at room temperature. ★

Why does a long excited-state lifetime give a sharp line?

long lifetime → energy more precisely defined → narrow range of photon energies → sharp spectral line

short lifetime → broad line, poorer resolution.

[Check] Why is EXAFS useful for a metalloprotein?

XAS is element-specific: tune to the metal's edge and see only the metal. EXAFS gives distances/number/type of atoms around the metal from ripples/oscillations after the edge + doesn’t need a crystal

Name 3 ways to get protein secondary structure from spectra

Far-UV CD (compare with standard curves); IR amide I/amide II band positions; (Raman amide bands ★). All sensitive to α-helix vs β-sheet.

[Check] A260 of a dsDNA solution is 0.50 (1 cm). Concentration?

Using 0.020 mL·µg⁻¹·cm⁻¹: c = A/(a·l) = 0.50/0.020 = 25 µg/mL.

[Check] Excitation polarised at 90° to μ - what happens?

No induced transition (no absorption), because the E-field cannot displace charge along μ.

[Bonus: VUV] What is vacuum UV (VUV) spectroscopy?

Absorption in ~125-240 nm (below ~200 nm needs vacuum/N₂ purge ★). Electronic transitions: σ→σ, n→σ, π→π*. Almost all molecules absorb (even small ones like water, oxygen) with unique spectra → fingerprints. VGA-100 VUV detector for GC introduced in 2014 (Schug et al.).

[Bonus: GC-VUV-MS] What are the 'complementary dimensions'?

GC separates by retention time (retention index); VUV gives an absorbance spectrum; MS gives m/z fragmentation. Combining the domains improves chemical identification

[Bonus: deconvolution] CLS vs SIMPLISMA-ALS vs LISA?

CLS (classic least squares): needs library spectra of components. SIMPLISMA-ALS: finds pure component spectra without a library, but can misassign features. LISA (Library-Integrated SIMPLISMA-ALS): SIMPLISMA → library search for starting conditions → ALS → component identification → reconstruction error estimation.

[Bonus: LISA] What problem does LISA fix?

Misassigned spectral features from SIMPLISMA-ALS, using library spectra to correct component identification.

[Bonus: VALID vs LISA] Compare accuracy and time

LISA (manual): 72/75 correct but >150 hours of operator time. VALID (automated): 63/75 correct (4/12 incorrect ones were close) in <1 hour of computing.

Why use spectroscopy to study materials?

A material's function doesn't follow directly from its chemistry. Spectroscopy links structure (how molecules form chemically, are arranged and interact) to properties, and shows how stimuli (temperature, force, water, light) change the molecular landscape and can be used to process/shape the material.

Example: why does silk degrade in nature but nylon doesn't?

Different molecular structure/interactions respond differently to stimuli. Spectroscopy shows which stimulus triggers degradation by revealing how the molecular landscape changes.

Example: how does nature combine stiffness and elasticity (silk)?

Synthetic materials are usually either stiff but not elastic, or elastic/rubbery but not stiff. Nature finds a unique molecular combination that gives both; spectroscopy helps explain it from the structure.

What are the two components of electromagnetic radiation?

An electric field component and a magnetic field component. The electric field describes how photons travel through space; it is drawn as a wave, polarised when we select a single plane.

What is radiant power?

How many photons hit the detector per unit time. P is proportional to the amplitude squared (P ∝ A²).

Key wave relations (frequency, speed of light, wavenumber)

ν = 1/period; c = νλ (in vacuum/air); wavenumber ν̄ = 1/λ (in cm⁻¹).

Energy of a single photon

E = hν = hc/λ = hcν̄ (h = 6.63·10⁻³⁴ Js). Energy increases when wavelength decreases (wavenumber increases).

What kind of change does each EM region cause?

Long wavelength/low energy = subtle: NMR/ESR change spin; microwave changes orientation (rotation); infrared changes configuration (bond vibrations); UV-vis and X-ray change electron distribution; γ-rays change nuclear configuration (dramatic).

Example: why do X-ray techniques work on crystals?

Atoms in a crystal are regularly spaced; X-rays interact with the electron distribution, so the signal reflects the regular electron density of the material.

What can happen when radiation hits a sample?

Reflection, transmission, absorption or scattering. We use these phenomena to extract information about the material.

Emission/chemiluminescence spectroscopy: how does it work?

Non-radiative energy (thermal, electrical, chemical) excites molecules to a higher state; when they relax they emit photons (radiant). Wavelength λ = identity of the species; emitted power P_E = concentration. No light source needed.

Photoluminescence (fluorescence) spectroscopy: how does it work?

A light source + wavelength selector irradiates the sample, molecules go to an excited state and emit light as they fall back. You detect the emitted light (not the transmitted excitation light). Energy differences between levels determine the wavelength λ.

Absorption spectroscopy: principle and equation

Incident energy P0 must match the energy gap between levels. A = −log T = −log(P/P0) = εbc (Beer-Lambert). Qualitative from λ (which bonds), quantitative from A (how much).

Beer-Lambert law: what are c, b and ε?

c = concentration, b = path length, ε = molar absorptivity.

Thick vs thin sample in transmission (4000-600 cm⁻¹)

A thick sample absorbs everything in some regions, so no light reaches the detector (saturation, ~0% transmission) and nothing can be concluded there. Fix: lower the concentration/path length (thinner sample) so that some light passes (A = εbc).

Continuum source vs line source

Continuum (e.g. a light bulb) has all wavelengths; changing wavelength is slow/gradual and gives poorly defined wavelength resolution. Line source: select one wavelength, switch it off and turn on another.

How does a monochromator select a wavelength?

Light with many wavelengths diverges and hits a concave mirror, which makes it parallel (collimated). A reflection grating disperses it by wavelength (angular dispersion); a second concave mirror focuses it onto the exit slit. Rotating the grating selects the wavelength.

Path of light in an FTIR interferometer

Source → slit → collimated beam → beam splitter (half transmitted, half reflected). One half goes to a stationary mirror, the other to a movable mirror; both return to the beam splitter, recombine and go through the sample to the detector.

When do the two beams interfere constructively/destructively?

Path difference δ = integer multiple of λ → constructive (waves in phase, stronger signal). δ = half-integer multiple of λ → destructive (signal cancels). Moving the mirror switches wavelengths on/off.

How do you get a spectrum from the interferometer?

Measure a blank without the sample first, then with the sample (the ratio removes the background). The detector records an interferogram (intensity vs mirror position); a Fourier transform converts it into the spectrum.

What determines spectral resolution in FTIR?

The mirror displacement: Δν̄ = 1/x. A larger displacement gives a finer resolution (e.g. x = 4 cm → 0.25 cm⁻¹). Tip: your notes link it to mirror step size; the slides link it to the maximum travel.

FTIR coupled to a microscope: what does it add?

You can use an aperture to select a small area of a thin slice (patient, animal, plastic) and measure spectra there. Different proteins/structures look different in space, giving much higher spatial resolution than a bulk measurement.

IR vs Raman: what is the difference?

IR = absorption of photons. Raman = inelastic scattering (the photon exchanges energy with the matter). Elastic = same energy in and out. They are complementary: bands missing in IR often appear in Raman.