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Magic of Light

Vladimir Lukashevich

theatrical lighting

stage lighting

<div class="raw-html-embed"><h3 id="fragment-magic-of-light">
    Fragment from the practical guide “Magic of Light,” published in 2013.
</h3>
</div><p>We’ve added a detailed table of contents to help you quickly locate key topics and to adapt this section of Vladimir Lukasevich’s classic work to an online format.</p><p>Vladimir Lukasevich (1956–2014) was an outstanding lighting designer who dedicated himself to scenography and working with light. This text is the result of his meticulous research and generalized stage experience.</p><p>We publish this material with the aim of conveying the value of his ideas and knowledge to a wide audience, with due respect to the personality and profession of the author.</p><p style="text-align:center;"><strong>! All exclusive rights to the original text belong to the family of Vladimir Lukasevich !</strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br><strong>Publication is carried out with the consent of the copyright holders.</strong></p><p>The presented text is intended for educational use.</p><p style="text-align:center;"><u>May the memory of this gifted artist continue to live in his works and inspire a new generation of theatre professionals.</u></p>

Vladimir Viktorovich Lukasevich - an outstanding lighting designer

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<div class="raw-html-embed"><h2 id="editors-preface">Editor’s Preface</h2></div>

<p>This section, Part 2: <i>Physics and Perception</i>, explains the physical and perceptual foundations of stage vision. It walks the reader through the nature and history of light (corpuscular vs. wave theories, electromagnetic theory), the photometric quantities used in lighting work (luminous flux, intensity, illuminance, luminance, exitance), and practical optical laws (reflection, refraction, transmission, inverse-square law).</p><p>It links physical measurements to human perception and gives practical examples relevant to stage lighting (e.g., side-lighting for dance).</p><p>The text also flags figures and equations that must be inserted verbatim from the original and ends with references and translator/editor notes about terminology and potential pitfalls.</p>

<div class="raw-html-embed"><h3 id="short-summary">Short summary (what this article contains)</h3>
</div>

<div class="raw-html-embed"><ol>
  <li>
    <p><strong>Prerequisites (brief):</strong> basic algebra, elementary trigonometry, comfortable with units (SI), and familiarity with common lighting equipment.</p>
  </li>
  <li>
    <p><strong>Stepwise plan:</strong></p>
    <ul>
      <li>Read the Light → Properties sections to become confident with photometric units (lumen, candela, lux, cd/m²).</li>
      <li>Study Luminance and Illuminance with an eye toward how measurements translate to perceived “brightness” on stage.</li>
      <li>Review Geometrical optics (reflection, refraction) and then the Inverse-square law; immediately apply with simple field measurements (luxmeter).</li>
      <li>Compare the theoretical notes with stage examples (side lighting for ballet, spotlight placement).</li>
      <li>Reinsert and study original figures/equations (placeholders are marked) — these are essential for accurate understanding.</li>
    </ul>
  </li>
  <li>
    <p><strong>Practical exercises (recommended):</strong></p>
    <ul>
      <li>Measure illuminance at several distances from a single fixture and verify the inverse-square law in practice.</li>
      <li>Photograph a surface under varied illuminance and compare perceived lightness vs. measured luminance.</li>
      <li>Test side-light placement in a rehearsal: alter distance and angle, observe uniformity across performers.</li>
    </ul>
  </li>
  <li>
    <p><strong>Follow-up reading:</strong> basic optics texts (Snell’s law, refractive index), CIE photometry short guides, and a short primer on human visual perception (photopic vs. scotopic vision).</p>
  </li>
</ol>
</div>

<div class="raw-html-embed"><h3 id="recommended-approach">Recommended approach to study (for stage lighting professionals)</h3></div>

<div class="raw-html-embed"><ol>
  <li>
    <p><strong>Figures and equations:</strong> many original mathematical expressions and diagrams appear as images in the Russian file. In the translated file these are marked as [IMAGE / EQUATION: …] and replaced with translated images to preserve correctness.</p>
  </li>
  <li>
    <p><strong>Terminology caution:</strong> the Russian «яркость» corresponds to luminance (L, cd/m²) in English; do not use the colloquial “brightness” where a precise photometric term is required. Similarly, «светимость» is luminous exitance (M, lm/m²) — do not confuse exitance with luminance.</p>
  </li>
  <li>
    <p><strong>Units &amp; constants:</strong> where definitions involve constants (for example, 1 lm = 1/683 W at 555 nm) the numbers are deliberate and standardized — keep them unchanged.</p>
  </li>
  <li>
    <p><strong>Translation fidelity:</strong> historical and personal names were anglicized (e.g., Thomas Young, Augustin-Jean Fresnel, Jean Foucault) for clarity; bibliographic entries retain original publication data.</p>
  </li>
  <li>
    <p><strong>Copyright &amp; use:</strong> this translation is intended for educational and professional reference; any republication must respect the copyright note at the head of this block.</p>
  </li>
</ol>

<p style="text-align:right; font-weight:700;">The original book «Magic of Light» was published by Sandrax.</p>

<p style="text-align:right;"><em>Enjoy reading</em></p>
</div>

<div class="raw-html-embed"><h2 id="editors-notes">Editor’s notes &amp; important footnotes</h2>
</div>

<ul><li><a href="#editors-preface">Editor’s Preface</a></li><li><a href="#fragment-magic-of-light">Fragment from the practical guide “Magic of Light,” published in 2013.</a></li><li><a href="#short-summary">Short summary (what this article contains)</a></li><li><a href="#recommended-approach">Recommended approach to study (for stage lighting professionals)</a></li><li><a href="#editors-notes">Editor’s notes &amp; important footnotes</a></li><li><a href="#part-2">PART 2. PHYSICS AND PERCEPTION.</a></li><li><a href="#light">LIGHT</a></li><li><a href="#properties-of-light">PROPERTIES OF LIGHT. UNITS OF MEASUREMENT.</a><ul><li><a href="#luminous-flux">LUMINOUS FLUX — LUMEN</a></li><li><a href="#solid-angle">SOLID ANGLE — STERADIAN</a></li><li><a href="#luminous-intensity">LUMINOUS INTENSITY — CANDELA</a></li><li><a href="#illuminance">ILLUMINANCE — LUX</a></li><li><a href="#luminance">LUMINANCE (traditionally called “brightness” in non-technical texts)</a></li><li><a href="#luminous-exitance">LUMINOUS EXITANCE (often called “luminous emittance” in older texts)</a></li></ul></li><li><a href="#principles-of-geometrical-optics">PRINCIPLES OF GEOMETRICAL OPTICS</a><ul><li><a href="#rectilinear-propagation">Rectilinear propagation and shadows</a></li><li><a href="#law-of-reflection">LAW OF REFLECTION</a></li><li><a href="#reflection-types">Reflection types</a></li></ul></li><li><a href="#transmission-absorption">TRANSMISSION AND ABSORPTION COEFFICIENTS</a></li><li><a href="#refraction">REFRACTION OF LIGHT</a></li><li><a href="#inverse-square-law">INVERSE SQUARE LAW</a><ul><li><a href="#formula-equals">Formula: E = I · cos θ / r²</a></li></ul></li></ul>

<p>We have already said that, just as a sculptor reveals a composition by cutting away the unnecessary from a block of stone, a lighting designer, by extracting objects and figures from darkness, reveals a stage composition to the audience. In this sense, stage lighting creates a “stage vision.” This process of “stage vision” is multi-stage and complex, and not all of its steps are unambiguously understood or exhaustively studied. After all, to this day the nature of light is not treated unambiguously: as a compromise between competing theories, it is accepted as exhibiting “wave–particle duality.”</p><p>If we break down the process of “stage vision” into its components, we obtain the following sequence: some light source emits luminous energy; that energy, after reflecting from surfaces located on the stage and refracting in the eye, reaches the retina.</p><p>The retina transforms the received energy into electrical impulses via a photochemical mechanism; those impulses travel along the optic nerve to the brain, which in turn does more than simply read those signals — it interprets them in a specific way. It is very important to understand that these stages are not connected in a strictly linear fashion. The mere fact that the image formed on our retina is inverted, yet we nevertheless perceive it correctly, demonstrates that the incoming signals are interpreted by the brain at an unconscious level. This is a small but telling example; below we discuss features of perception in greater detail. For now, it is important to note that each stage of seeing depends on the mechanism of that stage. A light source emits energy which, in our context, is transformed in many ways before it reaches the viewer’s eye, governed by physical laws — reflection, refraction, transmission, diffraction, etc. — then, upon reaching the eye, it is transformed according to the physiological particularities of vision, and afterwards it is also interpreted by the brain, taking into account not only psychological but, as we will see later, social experience of the person we call the viewer. It is likely impossible for a lighting designer to study in depth every facet of psychophysiology of visual perception — that is the job of other professions — but knowledge of the main laws and characteristics of the full chain of the “stage vision” process will allow a designer to make better and more precise decisions in the search for means to achieve their goals.</p>

<div class="raw-html-embed"><h2 id="part-2">PART 2. PHYSICS AND PERCEPTION.</h2>
</div>

<p>Early notions about the nature of light appeared among ancient Greek and Egyptian thinkers. As optical instruments were invented and improved (parabolic mirrors, the microscope, the telescope), those notions evolved and transformed.</p><p>At the end of the seventeenth century two theories of light arose: the corpuscular theory (Isaac Newton) and the wave theory (Robert Hooke and Christiaan Huygens).</p><p>According to the corpuscular theory, light is a stream of particles (corpuscles) emitted by luminous bodies. Newton believed that the motion of light corpuscles obeyed the laws of mechanics. Thus, reflection of light was understood analogously to the reflection of an elastic ball from a plane surface. Refraction was explained as a change in the velocity of corpuscles when they pass from one medium to another. For the case of refraction at the boundary vacuum–medium the corpuscular theory led to a formulation of the refraction law that implied a relationship between the speed of light in vacuum (c) and the speed of light in the medium (v).</p>

Original Corpuscular Theory Refraction Equation — Newton’s Optics

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[IMAGE / EQUATION: original corpuscular-theory refraction expression].jpeg

<div class="raw-html-embed"><h3 id="light">LIGHT</h3>
</div>

<p>The wave theory, in contrast to the corpuscular theory, treated light as a wave phenomenon, similar to mechanical waves. The basis of the wave theory was Huygens’s principle: every point reached by a wave becomes the center of secondary wavelets, and the envelope of those wavelets gives the position of the wavefront at the next instant. Using Huygens’s principle, the laws of reflection and refraction were explained.</p><p>For the case of refraction at the vacuum–medium boundary, the wave theory led to a different conclusion regarding the relationship between v and c. The law of refraction derived from the wave theory conflicted with Newton’s result: the wave theory predicted v &lt; c, whereas the corpuscular theory predicted v &gt; c.</p><p>Thus, by the beginning of the eighteenth century there were two opposing approaches to explaining the nature of light: Newton’s corpuscular theory and Huygens’s wave theory. Both explained the rectilinear propagation of light and the laws of reflection and refraction. The whole eighteenth century was a century of struggle between these theories. However, in the early nineteenth century the situation changed fundamentally. The corpuscular theory was rejected and the wave theory triumphed. Much credit for this goes to the English physicist Thomas Young and the French physicist Augustin-Jean Fresnel, who studied interference and diffraction. A complete explanation of these phenomena could only be given on the basis of the wave theory. Significant experimental confirmation of the wave theory came in 1851, when Jean Foucault measured the speed of light in water and obtained a value showing v &lt; c.</p><p>Although by the middle of the nineteenth century the wave theory was generally accepted, the question of the nature of light waves remained unresolved.</p>

Diagram of Huygens’ construction illustrating the direction of a refracted wave according to the wave theory of light

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Huygens’ constructions for determining the direction of the refracted wave.jpg

<p>In the 1860s James Clerk Maxwell established the general laws of the electromagnetic field, which led him to conclude that light is an electromagnetic wave. An important confirmation of this view was the coincidence of the speed of light in vacuum with the value derived from electromagnetic constants.</p>

Equation for the speed of light in vacuum from Maxwell’s electromagnetic theory

Equation for the speed of light in vacuum from Maxwell’s electromagnetic theoryjpeg

<p>The electromagnetic nature of light was further confirmed by Heinrich Hertz’s experiments on electromagnetic waves (1887–1888). At the beginning of the twentieth century, after Peter N. Lebedev’s experiments measuring light pressure (1901), the electromagnetic theory of light became firmly established.</p>

Formula showing the measured value of the speed of light c = 299792458 ± 1.2 m/s, confirming electromagnetic theory

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Precise Measurement of the Speed of Light (c = 299792458 m/s).jpeg

<p>An essential role in clarifying the nature of light was played by experimental determination of its speed. Beginning in the late seventeenth century, numerous attempts were made to measure the speed of light by various methods (astronomical methods such as those used by Ole Rømer and methods by Armand Fizeau, Albert A. Michelson). Modern laser techniques allow the speed of light to be measured with extremely high accuracy based on independent measurements of wavelength λ and frequency ν (c = λ · ν). This approach yielded a value whose accuracy surpasses earlier results by more than two orders of magnitude.</p><p>Light plays an extraordinarily important role in our lives. The overwhelming majority of information about the surrounding world reaches a human through light. In optics — the branch of physics dealing with light — the term “light” usually refers not only to visible light but also to adjacent ranges of the electromagnetic spectrum: infrared (IR) and ultraviolet (UV). Physically, light does not fundamentally differ from electromagnetic radiation in other spectral ranges — the portions of the spectrum differ only in wavelength λ and frequency ν.</p><p>For measuring wavelengths in the optical range we use the units nanometre (nm) and micrometre (µm):</p><p>1 nm = 10⁻⁹ m = 10⁻⁷ cm = 10⁻³ µm.</p><p>Visible light occupies approximately 400 nm to 780 nm, or 0.40 µm to 0.78 µm.</p><p>Electromagnetic theory of light explained many optical phenomena such as interference, diffraction, polarization, etc. However, this theory did not complete our understanding of light. At the beginning of the twentieth century it became clear that electromagnetic theory alone could not explain phenomena at atomic scales that occur when light interacts with matter. Explaining phenomena such as black-body radiation, the photoelectric effect, and the Compton effect required the introduction of quantum concepts. Science returned to the idea of corpuscles — light quanta. The fact that light shows wave properties in some experiments and particle properties in others means that light has a complex dual nature, commonly characterized as wave–particle duality.</p>

Diagram of the electromagnetic spectrum showing wavelengths, frequencies, and the visible light region from 400 to 750 nm

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<h3>LUMINOUS FLUX — LUMEN</h3><p>A fundamental photometric measure is luminous flux, denoted by the letter F.</p><p>Luminous flux is a measure of radiant power weighted by the spectral sensitivity of the human eye; it is defined as the amount of luminous energy passing through a unit area per unit time.</p><p>A lumen is defined as 1/683 of a watt of monochromatic radiation of frequency corresponding to a wavelength of 555 nm, which is at the peak of the photopic luminous efficiency function (the spectral sensitivity of the human eye under well-lit conditions). The value 1/683 was established historically when conventional light sources were compared to candles, and it has since been codified by international agreements.</p><p>The unit of luminous flux is the lumen (lm) (Latin — “light”): 1 lm is the luminous flux emitted by a point source with a luminous intensity of 1 candela into a solid angle of 1 steradian (assuming uniform distribution within that solid angle): 1 lm = 1 cd × 1 sr.</p><p>If we take a point source radiating uniformly in all directions and place a small area A in the path of the wave coming from that source, we can measure the energy passing through area A in time t.</p><p>Energy per unit time is called radiant power, or radiant flux. The power of luminous energy is characterized by luminous flux.</p><p>Examples — luminous flux of some light sources:</p><ul><li>Incandescent lamp 220 V, 100 W: 1000–1600 lm</li><li>Incandescent lamp 220 V, 1000 W: 17 000 lm</li><li>Incandescent lamp 110 V, 10 000 W: 295 000 lm</li><li>LED lamp 1 W: 120 lm</li><li>Flux falling on 1 m² of Earth’s surface on a clear sunny day: ≈ 100 000 lm/m²</li></ul>

Diagram showing luminous flux from source S through solid angle Ω to surface A, with energy ΔQ over time Δt

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<div class="raw-html-embed"><h2 id="properties-of-light">PROPERTIES OF LIGHT. UNITS OF MEASUREMENT.</h2>
</div>

<p>Light from sources — whether a simple match or a modern electric lamp — typically spreads more or less uniformly in all directions. However, using mirrors or lenses we can direct light and concentrate it into a particular region of space. The portion of space is characterized by a solid angle. Although the concept of solid angle has no direct linguistic connection to light, it is so widely used in lighting engineering that it is indispensable.</p><p>A solid angle is a portion of space bounded by a conical surface whose vertex is at the point of the light source.</p><p>The measure of a solid angle with its vertex at the center of a sphere is the ratio of the area of the spherical surface it subtends to the square of the radius of the sphere.</p><p>The unit of solid angle is the steradian (sr).</p><p>1 sr is the solid angle that subtends an area on the sphere equal to the square of the sphere’s radius. A cone with a solid angle of 1 sr has a vertex angle of approximately 65.5°. The unit of solid angle is the steradian (sr).</p><p>If a source is pointlike and radiates in all directions, its full solid angle is determined by the sphere’s full surface area. (Units of length and area used in calculation must be consistent.)</p>

Diagram showing solid angle Ω defined as area of a spherical segment A divided by the square of sphere radius R (Ω = A/R²)

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the central solid angle that cuts out a section of a sphere with an area equal to the square of its radius.jpg

<div class="raw-html-embed"><h3 id="solid-angle">SOLID ANGLE — STERADIAN</h3></div>

<p>Consider how much luminous flux falls into a unit solid angle:</p><p>The luminous flux per unit solid angle, when the flux is uniformly distributed within that solid angle, is called the luminous intensity of the source (I).</p><p>The radiometric analogue — radiant intensity — is defined similarly. For a point source whose dimensions are negligible compared to the distance to the observation point, the energetic radiant intensity I_e equals the ratio of radiant flux Φ_e to the solid angle Ω in which the radiation is distributed:</p><p>I_e = Φ_e / Ω</p><p>The unit of radiant intensity is watt per steradian (W/sr).</p>

<div class="raw-html-embed"><h3 id="luminous-intensity">LUMINOUS INTENSITY — CANDELA</h3>
</div>

<p>The photometric quantity luminous intensity is the spatial density of luminous flux in a given direction.</p><p>The unit of luminous intensity is the candela (cd) (from Latin candela — “candle”).</p><p>1 cd corresponds to the luminous intensity of a point source that emits a luminous flux of 1 lm uniformly distributed inside a solid angle of 1 sr. In 1948 the International Commission on Illumination (CIE) introduced a light standard based on a special emitter in which platinum is heated and melted by high-frequency currents. The candela is defined by the luminous intensity of such an emitter in the perpendicular direction from an area of 1/600 000 m² at the platinum freezing temperature T = 2045 K and standard pressure 101325 Pa.</p><p>Historically, the candle (cd) served as the main unit of luminous intensity; one spermaceti candle had an intensity of ≈ 1.005 cd.</p><p>The total luminous flux emitted in all directions characterizes an emitting source and cannot be increased by optical systems — they only redistribute flux, concentrating more into some directions while reducing it in others. That is how projectors increase luminous intensity along their axis while using sources of more modest intensity.</p>

Equation showing luminous intensity I equal to luminous flux Φ divided by solid angle Ω; with note on candela definition

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Formula for luminous intensity I = Φ/Ω.jpg

<p>In practice we deal with real sources whose flux distribution is not uniform in all directions (for example, spotlights, flashlights, or incandescent lamps with a reflective back). Therefore, the luminous intensity of any point-like emitter must be specified with direction.</p><p>Often the luminous intensity distribution of a source is shown graphically. The spatial distribution of luminous intensity is uniquely determined by the photometric body — the part of space bounded by the surface through the tips of the radius vectors of luminous intensity. If we cut the photometric body with a plane passing through the origin, we obtain the intensity distribution curve (also called the light distribution curve, or LDC) for that plane as a planar polar diagram.</p>

Graphs showing luminous intensity distribution curves (LDC) of spotlights PO 07-250 and PO 07-400, illustrating variation of luminous intensity with angle

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Light distribution curves of two spotlights PO 07-250 and PO 07-400.jpg

<p>In a Cartesian coordinate system, the horizontal axis represents angles relative to the axis of maximum emission; the vertical axis represents luminous intensity. In polar coordinates, the axis of maximum intensity is vertical and angles are measured from it. Lines of equal intensity form concentric circles; measured intensity values at each angle are plotted and then connected to form the characteristic “petal” shape.</p><p>A linear coordinate system is suitable for sources with small solid angles (i.e., narrow beams, such as spotlights) where the horizontal scale can be limited (for example, −20° to +20° instead of −90° to +90°). If a source is asymmetric — as is the case with a long linear lamp — LDCs for two planes (vertical and horizontal) are given. Then the spatial “petal” graph becomes elliptical in cross section.</p>

Set of six polar diagrams showing luminous intensity distribution of LED linear floodlight in different configurations: with lenses at various positions and without lenses, illustrating beam shape and intensity changes

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<p>Illuminance is the luminous flux incident on a surface per unit area. If a luminous flux Φ falls on area S, the mean illuminance E of that area (denoted by E) equals E = Φ / S. The unit of illuminance is the lux (lx).</p><p>1 lx is the illuminance produced by a flux of 1 lm uniformly distributed over an area of 1 m².</p><p>&nbsp;</p>

Equation showing illuminance E equal to luminous flux Φ divided by area A, with unit lux defined as lumen per square meter (lm/m²)

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Formula for illuminance E = Φ/A in lux.jpg

<div class="raw-html-embed"><h3 id="illuminance">ILLUMINANCE — LUX</h3>
</div>

<p>If the luminous flux from a point source is Φ and it falls at distance r on a surface oriented at an angle θ to the direction of the light, then for a point source the illuminance E is given by the inverse-square relation combined with the cosine of incidence:</p>

Equations showing relation between luminous flux Φ, luminous intensity I, solid angle Ω, surface area A, and distance r, leading to illuminance E = I / r²

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Formula for illuminance and the inverse-square law.jpg

<p>E = I · cos θ / r²</p><p>If several sources illuminate a surface from different directions, total illuminance at a point is the sum of illuminances from each source:</p><p>E = E₁ + E₂ + E₃ + … + Eₙ.</p><p>This is the law of additivity: total illuminance equals the algebraic sum of the contributions from all sources.</p><p>Illuminances produced by natural sources (approximate):</p><ul><li>Direct sunlight (summer): ~100,000 lx</li><li>Direct sunlight (winter): ~10,000 lx</li><li>Overcast sky (summer): 5,000–20,000 lx</li><li>Overcast sky (winter): 1,000–2,000 lx</li><li>Full moon (night): ~0.2 lx</li><li>Clear moonless night sky: ~0.0003 lx</li></ul><p>Suppose the illuminance at a desk is 100 lx. On the desk lie sheets of white paper, a black folder, and a book with a gray cover. The illuminance of all these objects is the same, yet the eye perceives the paper as lighter than the book, and the book as lighter than the folder. That is, our eye does not judge the lightness of objects by illuminance alone, but by another quantity — luminance.</p>

Illustration showing point source S at distance r producing illuminance E₀ = I/r² and Ea = (I/r²)·cos α on a surface, demonstrating cosine law and inverse-square law for light distribution

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Diagram of illuminance with cosine law and inverse-square relation.jpg

<p>Luminance of a surface S in a given direction is the ratio of the luminous intensity emitted by that surface in that direction to the area of the projection of that surface onto a plane perpendicular to the chosen direction. Projection area equals the actual area multiplied by the cosine of the angle between the surface and the projection plane. While luminous flux, luminous intensity, and illuminance have special unit names (lumen, candela, lux), the unit for luminance is simply candela per square meter (cd/m²) — colloquially sometimes called a “nit” in older literature. The SI uses cd/m² for luminance.</p><p>What determines the luminance of objects? Many practical sources are not pointlike, and their dimensions are visible; for such sources we use the concept of source luminance. The concept of luminance also applies to reflecting surfaces and screens, which can be treated as sources, provided the luminous intensity is determined taking into account the surfaces’ reflective properties.</p>

Illustration showing luminance calculation: luminous intensity Iα emitted at angle α divided by the projection area A·cos α, with formula La = Iα / (A·cos α) and unit candela per square meter (cd/m²)

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Diagram and formula for luminance of a surface in a given direction.jpg

LUMINANCE (traditionally called “brightness” in non-technical texts)

<p>&nbsp;</p><h3>ILLUMINANCE — LUX</h3>

<p><i>Luminance varies with direction for a given source — it characterizes emission in a particular direction.</i></p><p>For a diffusely reflecting (matte) surface, luminance is simply related to the illuminance by:</p><p>L = ρ · E / π,</p><p>where ρ is the reflectance (the fraction of incident flux reflected by the surface).</p><p>Luminance is the only photometric quantity that the eye perceives directly; in the absence of absorption in the propagation medium, luminance does not depend on distance.</p><p>The relation linking object luminance L, the illuminance E_eye produced by that object on the pupil of the eye, and the solid angle Ω subtended by the object as seen by the eye can be written:</p><p>L = E_eye / Ω.</p><p>Therefore, when the eye moves away from an object, the illuminance E_eye on the pupil decreases, and the subtended solid angle Ω also decreases, but the luminance L of the object remains unchanged.</p><p>Typical luminances (order of magnitude):</p><ul><li>Night, moonless sky: ≈ 1 × 10⁻⁴ cd/m²</li><li>Neon lamp: ≈ 1 × 10⁸ cd/m²</li><li>Full moon as seen through atmosphere: ≈ 2.5 × 10³ cd/m²</li><li>Flame of an ordinary stearin candle: ≈ 5 × 10³ cd/m²</li><li>Clear sky (day): ≈ 1.5 × 10⁴ cd/m²</li><li>Gas-discharge lamp: ≈ 5 × 10⁴ cd/m²</li><li>Metal filament of an incandescent lamp: ≈ (1.5–2) × 10⁶ cd/m²</li><li>Filament coil of gas-filled incandescent lamp: ≈ 5 × 10⁶ cd/m²</li><li>Regular carbon arc crater: ≈ 1.5 × 10⁸ cd/m²</li><li>Sun: ≈ 1.5 × 10⁹ cd/m²</li><li>Capillary mercury arc (very high pressure): ≈ 1.5 × 10⁹ cd/m²</li><li>High-pressure mercury lamp (spherical arc): ≈ 4 × 10⁸ cd/m²</li><li>Pulsed strobe lamp (impulse): ≈ 1.2 × 10⁹ cd/m²</li><li>Extremely intense pulsed source: ≈ 1 × 10¹¹ cd/m²</li></ul>

Luminance diagram showing observer’s eye viewing luminous plane Siz as projected plane Sif perpendicular to line of sight

medium_In the figure, the observer's eye sees a luminous plane Siz, but it seems to him that he is observing a plane Sif, which is perpendicular to the axis of his vision. (1).jpg

small_In the figure, the observer's eye sees a luminous plane Siz, but it seems to him that he is observing a plane Sif, which is perpendicular to the axis of his vision. (1).jpg

thumbnail_In the figure, the observer's eye sees a luminous plane Siz, but it seems to him that he is observing a plane Sif, which is perpendicular to the axis of his vision. (1).jpg

xsmall_In the figure, the observer's eye sees a luminous plane Siz, but it seems to him that he is observing a plane Sif, which is perpendicular to the axis of his vision. (1).jpg

In the figure, the observer's eye sees a luminous plane Siz, but it seems to him that he is observing a plane Sif, which is perpendicular to the axis of his vision.jpg

<p>Luminous exitance (M) characterizes the luminous flux leaving a luminous surface per unit area.</p><p>Luminous exitance is numerically equal to the luminous flux emitted by a small considered area (an equal-luminance element) divided by the area of that element.</p><p>The unit of luminous exitance is lumen per square meter (lm/m²), which is dimensionally identical to lux. One commonly used definition takes as a unit the luminous exitance of a surface that emits 1 lm per m².</p>

Formula for luminous exitance M = Φ / A in units of lm/m²

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Luminous Exitance: definition, formula, and units (M = Φ / A, lm/m²).jpeg

<div class="raw-html-embed"><h3 id="luminous-exitance">LUMINOUS EXITANCE (often called “luminous emittance” in older texts)</h3>
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<p>In a homogeneous transparent medium, light rays are straight lines.</p><div class="raw-html-embed"><h3 id="rectilinear-propagation">Rectilinear propagation and shadows</h3>
</div><p>Rectilinear propagation of light is illustrated by the formation of shadows. If an opaque object lies in the path of light rays, then:</p><ul><li>A ray that passes by the object continues in its original direction as if the object were not present.</li><li>A ray that strikes the object does not pass through it; its propagation along that line is blocked.</li></ul><p>This produces a geometric shadow. Because light propagates rectilinearly, the shape of the geometric shadow will resemble the contour of the object.</p><p>The smaller the dimensions of the light source, the sharper and clearer the shadow’s outline on a screen or backdrop. For larger sources the shadow becomes blurred, because rays from different points on the source produce slightly shifted shadows whose superposition gives a softer edge.</p><p>Light rays cross each other without affecting one another; each ray illuminates space independently.</p>

Diagram illustrating the law of reflection, showing that the angle of incidence (α) is equal to the angle of reflection (β).

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Diagram illustrating the law of reflection.jpg

<div class="raw-html-embed"><h2 id="principles-of-geometrical-optics">PRINCIPLES OF GEOMETRICAL OPTICS</h2>
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<p>1. The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.</p><p>2. The angle of reflection equals the angle of incidence: α = β.</p><p><i>Reflection coefficient</i> — the ratio of the luminous flux reflected by a surface to the luminous flux incident upon it from a given light source or luminaire. The higher the reflectance coefficient, the brighter the surface appears. In the desk example above the paper has a higher reflectance than the book cover, which in turn has a higher reflectance than the folder. Reflectance depends both on the material properties and on surface finish.</p>

Diffuse reflection diagram showing scattered rays from a rough surface

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<div class="raw-html-embed"><h3 id="law-of-reflection">LAW OF REFLECTION</h3>
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<p>Reflection may be directional (specular) or diffuse within a certain solid angle. Take ordinary white paper: it appears similarly bright from any viewing angle, i.e., its luminance is approximately the same for all directions — this is diffuse reflection.</p><p>Diffuse or scattered reflection occurs from matte paper, most fabrics, matte paints, whitewash, rough metals, etc. If we polish a rough metal surface, its reflection character changes: if polished very well, all incoming light reflects in a single direction and the angle of reflection equals the angle of incidence — this is specular reflection. Specular and diffuse reflections are the two extremes; intermediate cases (directionally scattered or mixed reflection) occur for poorly polished metals, silk, glossy paper, and frosted glass.</p><p>For diffusely reflecting surfaces the luminance is related to illuminance by the simple relation:&nbsp;<br>L = ρ · E / π.</p><p>For directionally scattered or mixed surfaces one needs the actual reflection indicatrices (bidirectional reflectance distribution functions — BRDFs) to predict luminance.</p><p>The four photometric quantities described above — luminous flux, luminous intensity, illuminance, and luminance — are essential for understanding the behavior of light sources and luminaires. But to fully characterize the photometric properties of materials one must also know coefficients such as reflectance, transmittance, and absorptance.</p>

Diagrams of light reflection types: specular, directional scattered, diffuse, mixed

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<div class="raw-html-embed"><h3 id="reflection-types">Reflection types</h3></div>

<p>The fraction of light that passes through a material is characterized by the transmittance (transmission coefficient), and the fraction absorbed is characterized by the absorption coefficient. For any material, the sum of reflectance, transmittance, and absorptance equals unity. There is no real material with any of those three coefficients equal to 1. High diffuse reflectance is found in fresh snow, chemically pure barium sulfate, and magnesium oxide. Highest specular reflection is found in polished silver and specially treated aluminum.</p>

<div class="raw-html-embed"><h2 id="transmission-absorption">TRANSMISSION AND ABSORPTION COEFFICIENTS</h2>
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<p>When a light beam strikes the boundary between two transparent media of different optical densities (for example, air and water), part of the light is reflected and part enters the second medium. Upon entering the second medium the ray changes direction at the boundary — this is refraction.</p><p>If light falls from an optically less dense medium into a more dense medium, the refracted angle is always smaller than the incident angle.</p><p>Transmittance values are typically tabulated for a reference thickness (commonly 1 cm). Highly transparent materials include pure quartz and certain grades of PMMA (acrylic). Light transmission, like reflection, can be specular (directional), diffuse (e.g., milk glass), directionally scattered (e.g., etched glass), or mixed.</p><p>Most materials reflect, transmit, and absorb light differently at different wavelengths — this wavelength dependence determines their color. Spectral characteristics of reflectance, transmittance, and absorptance are needed to fully describe photometric properties. All three coefficients are dimensionless and usually expressed as fractions or percentages.</p><p>&nbsp;</p>

Diagram showing light refraction when passing through air, water, and glass with incident and refracted rays

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<div class="raw-html-embed"><h2 id="refraction">REFRACTION OF LIGHT</h2>
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<p>The first law of photometry — the inverse-square law — was formulated by Johannes Kepler in 1604.</p><h3>Formula: E = I · cos θ / r²</h3><p>where:</p><ul><li>E — illuminance</li><li>r — distance from the source to the object</li><li>I — luminous intensity of the point source</li><li>θ — angle of incidence relative to the surface normal&nbsp;</li></ul><p>This law is probably the most intensively used principle by lighting designers. Whether consciously or intuitively, it is present in our decision chain. When we choose the type of instrument to place at a certain position, or choose the mounting point for a lamp, or when evaluating the picture we have created, we must always keep in mind how different the view will be for audience members in the stalls versus the balcony.</p><p>The key word in the law’s formulation is relative: the law is meaningful for comparing illuminance at two different distances. Units (feet or meters) do not change the qualitative relationships. Practically, the inverse square law means:</p><ul><li>Doubling the distance reduces illuminance by four times.</li><li>Tripling the distance reduces illuminance by nine times.</li><li>Halving the distance increases illuminance by four times.</li></ul>

Diagram showing the inverse square law of light, illustrating how illuminance decreases with distance (r, 2r, 3r) from a point source

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<div class="raw-html-embed"><h2 id="inverse-square-law">INVERSE SQUARE LAW</h2>
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<p><span style="background-color:transparent;color:#000000;">Еxamines the physics and perception of stage lighting, tracing historical theories of light and explaining photometric units, optics (reflection, refraction, inverse-square law), and human visual response, with practical guidance for designers, technicians, and choreographers to create clearer, more consistent stage images.</span></p>

<p><span style="background-color:transparent;color:#000000;">Еxamines the physics and perception of stage lighting, tracing historical theories of light and explaining photometric units, optics (reflection, refraction, inverse-square law), and human visual response, with practical guidance for designers, technicians, and choreographers to create clearer, more consistent stage images.</span></p><p><br>&nbsp;</p>

#stage-lighting

Fragment from the practical guide “Magic of Light,” published in 2013.

Stage lighting–sound integration: techniques, perception, history, and creative design

Section: What does a lighting designer create? A dynamic communicative environment