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Primary pressureless spherical-collapse calculation distinguishing finite comoving collapse time from the distant-coordinate description and progressively redshifted escaping light. Physical Review 56, 455–459 (1939). doi.org/10.1103/PhysRev.56.455

Optical activity is the ability to rotate the direction of linear polarization of transmitted light. In an achiral solvent, the two members of an enantiomer pair have equal and opposite optical rotations at the same wavelength, temperature and concentration. The measured angle concerns a bulk sample; it is not a geometric rotation of the molecules.^[ref]

The rotating object in this description is the direction along which the electric field oscillates. At each position the transmitted light can still have linear polarization: its electric field moves back and forth along a line, while the orientation of that line changes along the sample. Nothing requires the molecules to turn bodily through the observed angle. This makes polarimetry a bridge from molecular chirality to a visible bulk measurement, and, with a suitable calibration, a way to follow concentration or the balance of enantiomers.

In a transparent, isotropic chemical solution, natural optical rotation can be understood as circular birefringence: the two opposite circular polarizations accumulate different wave phases, and their equal-amplitude sum remains linearly polarized along a rotated direction. Circular dichroism instead means unequal absorption of those components and can produce elliptical polarization. These are related responses, not interchangeable measurements. General birefringence need not produce this simple rotation of linear polarization.^[ref]

An optical chopper periodically interrupts a beam of light, for example with a rotating slotted wheel. Its timing can provide a reference for a lock-in amplifier measuring the modulated photodiode signal.

Optical coherence describes correlations between the wave amplitudes and wave phases of light sampled at different places or times. Its most direct classical test is wave interference: combine two samples of a field and see how much the detected light intensity changes when their relative wave phase is scanned. First-order optical coherence makes this statement quantitative; temporal optical coherence compares delayed samples, while spatial optical coherence compares different positions. These properties are relative to the samples and averaging procedure, rather than a single yes-or-no label for a source. ^[ref].

A useful surprise is that two copies of a fluctuating source can interfere strongly when they have matched delays: the copies share the fluctuations. Conversely, two individually steady-looking beams need not have correlated wave phases. The ideal diffraction grating calculation requires spatial optical coherence across its illuminated elements; unequal-arm measurements with a Michelson interferometer test temporal optical coherence.

An optical concentrator redirects light from an entrance area $A_{\mathrm{in}}$ to a smaller receiver area $A_{\mathrm{out}}$. Its geometric concentration ratio is $C=A_{\mathrm{in}}/A_{\mathrm{out}}$. Specify the admitted angular distribution and losses before interpreting $C$ as an irradiance gain: if a fraction $\eta$ of incident radiant flux reaches the receiver, the ratio of mean receiver to mean entrance irradiance is $\eta C$.

Optical-electrical heating non-equivalence means that equal absorbed optical and electrical powers do not necessarily give identical thermometer responses. Light and the heater may deposit heat in different places, producing different temperature gradients and different routes of thermal conduction to the support. Holding one thermometer reading fixed need not hold every part of the cavity at the same temperature. This differs from incomplete radiometric absorptance: one concerns where absorbed heat goes, the other how much incident light becomes absorbed heat.

A useful accounting convention iswhere the signed correction ${\delta }_{\mathrm{ne}}$ is determined by characterization of the instrument and represents the residual departure from the lumped electrical substitution heat balance. It is not a universal extra source of energy. Varying the beam location or heater location, comparing equivalent temperature excursions, and checking repeatable dark returns can test the assumptions; no single small correction proves that every other correction vanishes.

An optical fiber is a thin, flexible electromagnetic waveguide that carries light along its length. In a conventional step-index optical fiber, an optical fiber core with refractive index $n_1$ is surrounded by an optical fiber cladding with lower refractive index $n_2$. Suitable light rays remain confined by total internal reflection at this interface. The cladding is an optical part of the guide, distinct from its protective coating.^[ref]

The useful surprise is that a transparent strand can deliver light around a route that a free beam would leave. This makes optical fibers useful for communications and for carrying collected light to a fiber-fed spectrograph. Guidance, successful launch, and surviving optical power are separate questions: the optical fiber acceptance angle constrains launch geometry, while optical fiber attenuation describes loss along the route.

MIT's Optical Waveguides and Fibers, Laboratory Exercise No. 7 (Fall 2005), describes a teaching apparatus. A cleaned, flat-ended multimode optical fiber receives helium–neon laser light through a microscope objective optical lens; a micropositioner aligns the input. The launch deliberately overfills the fibre's cone. A beam splitter sends a sample to a reference photodetector to track laser fluctuations. The fixed output faces a screen or a photodetector on a rotation stage with angular measurement calibration. Readings every two degrees, divided by simultaneous reference readings, give an angular profile. Repeating with an underfilled launch is a control: too few excited normal modes underestimate numerical aperture. Optional index-matching fluid removes cladding-carried light. Bending the fibre reveals leakage and reduced output on an oscilloscope. The handout supplies no measured trace or absolute detector measurement calibration, and this angular scan does not determine loss per kilometre.^[ref]

Guiding light and retaining useful optical power are different achievements. Charles Kuen Kao and George Alfred Hockham argued that impurities need not impose the measured losses of existing glasses on every future optical fiber. Their 1966 paper treats wave absorption, scattering of light and guidance separately; reducing impurity absorption leaves intrinsic material losses and geometric losses to address. This was a route toward practical communication, building on existing optical fibers, rather than the invention of every use of guided light.^[ref]

The launch experiment used clad glass optical fibers fixed in capillary tubes with epoxy for end polishing. Laser illumination gave transverse normal mode patterns; input-spot displacement and polarization of an electromagnetic wave controlled excitation. These observations tested guidance, not kilometre-scale optical fiber attenuation.^[ref]

Charles Kuen Kao's lecture describes the complementary material experiment: short, polished glass samples, including plasma-deposited fused silicon dioxide, were examined with purpose-built single-beam and later double-beam spectrophotometers. A separate ellipsometry measurement assessed end-surface specular reflection, a check against confusing interface loss with bulk wave absorption. The readout was loss versus wavelength. Comparing glass samples supported impurity reduction as a route to lower loss. Surface contamination and the tiny bulk loss of short samples limited inference; the result did not itself demonstrate a long drawn optical fiber. The lecture also credits subsequent manufacturing work at Corning.^[ref]

An original scale comparison makes the material problem tangible. In the uniform optical fiber attenuation model, a stipulated $20dB/km$ leaves $10^{-2}=0.01$ of launched optical power after $1\mathrm{km}$; a stipulated $0.2dB/km$ leaves $10^{-0.02}\simeq 0.95499$. Both guides could satisfy the same total internal reflection condition. A successful spot pattern at the output therefore cannot by itself establish a useful communication distance.

An optical filter selectively transmits light according to properties such as wavelength or polarization of waves.

Optical gain is amplification of light by a medium. Here the small-signal intensity gain coefficient $g$ has units ${\mathrm{m}}^{-1}$: for fixed populations, a weak beam obeysin the nondegenerate resonant two-level model, with common transition cross-section $\sigma$. Thus $g$ includes the competition between stimulated emission and photon absorption on that transition. Separate passive intensity loss $\alpha$ gives $I(z)=I(0)e^{(g-\alpha )z}$. Both coefficients describe light intensity, not wave amplitude; the corresponding field-amplitude exponent is half as large. ^[ref].

For $g=0.30{\mathrm{m}}^{-1}$, $\alpha =0.10{\mathrm{m}}^{-1}$ and $z=0.50\mathrm{m}$, the single-pass intensity multiplier is $e^{0.10}\approx 1.10517$. This is amplification during one passage, before mirror losses. Population inversion can therefore yield positive optical gain while the complete oscillator remains below laser threshold.

Measurement using interfering light fields. A phase difference changes the detected intensity, allowing measurements of displacement, optical path length or a spectrum. The round-trip phase in a Michelson interferometer gives one explicit path-to-phase calibration; Fourier transform spectroscopy recovers spectral information from an interferogram.

An optical isolator transmits light preferentially in one direction. An ideal Faraday effect device combines a $45^{\circ }$ rotator with polarizers at $0^{\circ }$ and $45^{\circ }$: forward light passes, while backward light acquires another $45^{\circ }$ rotation and reaches the entrance polarizer at $90^{\circ }$. See Faraday rotation on a round trip.

An optical microscope uses light and optical lens assemblies to reveal small structures, such as the boundaries of biological cells or defects in a manufactured surface. In a compound optical microscope, the microscope objective supplies an enlarged real image; the microscope eyepiece makes that intermediate microscope image subtend a larger viewing angle. The transverse magnification of the first stage and the angular magnification of the second answer different questions.^[ref]

Consider an original ideal finite-conjugate microscope in air, with both optical lens assemblies treated as converging thin lens elements in the paraxial approximation. Choose objective focal length $f_o=10\mathrm{mm}$ and object distance $u_o=12\mathrm{mm}$. The thin lens equation and signed transverse magnification givePlace a microscope eyepiece of focal length $f_e=25\mathrm{mm}$ a further $25\mathrm{mm}$ beyond the intermediate microscope image. The objective-to-eyepiece separation is therefore $85\mathrm{mm}$. Each object point then supplies a parallel outgoing bundle of light rays, appropriate to a relaxed eye focused at infinity. Define the unaided reference as the same object viewed at distance $D=250\mathrm{mm}$; this is a rating convention, not a universal property of eyesight. The eyepiece angular magnification and total signed angular magnification areFor instance, a hypothetical object height $h_o=0.020\mathrm{mm}$ becomes $h_i=-0.100\mathrm{mm}$ at the intermediate microscope image. The signed viewing angles are approximately $h_i/f_e=-0.004\mathrm{rad}$ with the instrument and $h_o/D=0.00008\mathrm{rad}$ unaided. Their ratio is $-50$: enlarged and inverted. These are stipulated model dimensions, not measurements or specifications of a modern commercial optical microscope.

The attraction of an optical microscope is that seeing can become measuring: a stage micrometer supplies a known object-space length, and microscope scale calibration converts an image readout into a specimen length. This also separates a large-looking image from a trustworthy size estimate. Meanwhile, diffraction-limited resolution depends on numerical aperture and wavelength; empty magnification enlarges an existing blur without revealing additional structure.

Steven Chu's Bell Laboratories team prepared sodium atoms by pulsed-laser evaporation of a pellet. A frequency-swept opposing beam slowed them before six crossed laser beams supplied optical molasses. The vacuum chamber used a shield coated with graphite and cooled with liquid nitrogen as a pump. Fluorescence provided the readout; the initial beams were aligned as closely counterpropagating as possible. ^[ref].

After equilibration, the team switched off the cooling light for a variable interval, then restored it. Faster atoms escaped during the dark interval; slower atoms were recaptured. The recaptured fraction versus delay constrained the velocity distribution and hence temperature. The inference depended on the initial cloud shape and recapture volume: Steven Chu later acknowledged adjusting a geometry correction towards the expected Doppler cooling limit. Delay was the scanned variable, and the cooling beams themselves supplied the release/recapture control; visible fluorescence alone could not establish temperature. ^[ref].

An optical pulse is a finite-duration envelope of light. A nearly monochromatic pulse has many carrier oscillations within its duration $\tau$: in units with light speed one, its wavelength obeys $\lambda \ll \tau$. A slowly varying propagation-time map stretches the pulse duration by its derivative and divides the observed frequency by the same factor.

// Target: general-relativity.bigb

Circular polarization selects the sign of the absorbed photon's angular momentum along the beam. Choose that direction as $z$ and define ${\sigma }^{+}$ by the absorption rule $m^{\prime }=m+1$, where $m$ is the magnetic quantum number. Spontaneous emission can return an atom to a different magnetic sublevel, so absorption followed by emission is a population-transfer cycle. A sublevel that the chosen beam cannot excite is dark to that beam. Darkness is relative to the selected transition and electromagnetic polarization, rather than a claim that the atom cannot interact with any light.

A static magnetic field along $z$ defines a stable axis and gives Zeeman splitting. A transverse oscillating magnetic field can redistribute magnetic sublevel populations when its frequency matches an allowed splitting. With the appropriate optical transition, that redistribution restores photon absorption: transmitted intensity decreases, or collected fluorescence increases. These are alternative readouts whose detailed sensitivity depends on the transition, viewing direction and electromagnetic polarization.

Redirection of incident light into outgoing directions at a material boundary or through scattering near it. Specular reflection concentrates light around a geometric reflection direction; diffuse reflection distributes it more broadly. This physical process is distinct from reflection as a mathematical transformation.

Optical rotation is the signed angle measured in polarimetry. Positive rotation is clockwise for an observer facing the incoming light; negative rotation is counterclockwise. State the viewing convention, wavelength, temperature, solvent, concentration and path length when comparing measurements. R and S configuration specifies spatial arrangement, and does not predict the sign of optical rotation.^[ref]

Here the observer stands beyond the sample, on the detector side, looking back toward the source. Measure both the polarimeter analyzer angle $\theta$ and the optical rotation $\alpha$ clockwise from the blank's polarization direction. Looking from the source end reverses the apparent sense. A line has no distinguished arrowhead, so an intensity scan alone determines its orientation only modulo $180^{\circ }$; continuity or additional information must choose the appropriate rotation branch.

An optical scattering force transfers momentum from light to a particle through scattering of light. In a usual single-beam optical trap, its axial contribution pushes along beam propagation; the optical gradient force must balance it for axial confinement. This balance can place the stable equilibrium away from the beam focus.