Summary 7EB1B20 Physics of Light and Lighting Design
Chapter 1 – Photometry (5Q)
Summary information
Light is a form of electromagnetic radiation with wavelengths between 380 nm (violet) and 780
nm (red).
The visible spectrum includes:
Violet (380-420 nm) Green (495-566 nm) Red (627-780 nm)
Indigo (420-450 nm) Yellow (566-589 nm)
Blue (450-495 nm) Orange (589-627 nm)
Beyond visible light:
→ Infrared (longer wavelength, felt as heat)
→ Ultraviolet (shorter wavelength, can damage skin/eyes)
Photometry = the science of measuring light according to human eye sensitivity functions (CIE –
International Commission on Illumination)
→ Unlike radiometry (which measures all electromagnetic radiation), photometry specifically
focuses on visible light and how humans perceive it
The retina contains specialized cells called photoreceptors that convert light into neural signals.
There are two main types of photoreceptors:
→ Cones (~5 million): Active in higher light levels, responsible for color perception. – photopic
vision (daylight)
o L-cones: Sensitive to long wavelengths (564 nm) – red
o M-cones: Sensitive to medium wavelengths (534 nm) – green
o S-cones: Sensitive to short wavelengths (420 nm) – blue
→ Rods (~110 million): Active in low light conditions, highly sensitive to brightness but not
color – cannot distinguish colors – scotopic vision (night vision)
Spectral Sensitivity – the human eye's sensitivity varies with wavelength:
→ Peak sensitivity at 555 nm for photopic vision (daylight, cones) – GY – V(λ) function
→ Peak sensitivity at 507 nm for scotopic vision (night vision, rods) – BG – V’(λ) function
→ 540×1012 Hz is the frequency of green light
Quantity Definition Symbol Unit Formula
Luminous Total amount of light Фv lm (lumen) 𝑄𝑄𝑣𝑣
𝜙𝜙𝑣𝑣 =
emitted by a source in
flux all directions 𝑡𝑡
𝜙𝜙𝑣𝑣 = 𝐾𝐾𝑚𝑚 ∙ � 𝜙𝜙𝑒𝑒,𝜆𝜆 ∙ 𝑉𝑉(𝜆𝜆) ∙ ∆𝜆𝜆
𝐾𝐾𝑚𝑚 = max. photometric equivalent of
radiation = 683 lm/W
𝜙𝜙𝑒𝑒 = radiant flux (mW/nm)
Luminous Amount of light Iv cd 𝐼𝐼𝑣𝑣 =
𝜙𝜙𝑣𝑣
emitted in a specific
intensity direction
(candela) = Ω
lm/sr Ω = solid angle (sr – steradians)
𝐴𝐴
Ω= a full sphere: 4π sr
𝑟𝑟 2
, Luminous Different light sources η lm/W 𝜂𝜂 =
𝜙𝜙𝑣𝑣
convert electrical
efficacy power to light with 𝑃𝑃
- 10 lm/W – incandescent lamp
varying efficiencies
- 60 lm/W compact fluorescent lamp
(indicator for energy
(CFL)
efficiency of a lamp)
- 150 lm/w LED lamp – can exceed
𝐾𝐾𝑚𝑚 = max. luminous efficacy of
radiation = 683 lm/W
Illuminance Amount of light Ev lx (lux) = 𝐸𝐸𝑣𝑣 =
𝜙𝜙𝑣𝑣
falling on a surface - Ehor – measured on lm/m2 𝐴𝐴
horizontal surfaces (desk) 𝐴𝐴 = area
– important in general
tasks (reading)
- Ever – measured on
vertical surfaces (walls) –
important in sports field
Luminance Perceived brightness Lv cd/m2 𝐼𝐼𝑣𝑣
of a surface 𝐿𝐿𝑣𝑣 =
𝐴𝐴𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
𝐴𝐴𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝐴𝐴 ∙ cos (𝜀𝜀1 )
Luminous Total amount of light Qv lms or
that a lamp can 𝑄𝑄𝑣𝑣 = � 𝜙𝜙(𝑡𝑡) 𝑑𝑑𝑑𝑑
energy produce over its lmh ∆𝑡𝑡
lifetime by weighing
its luminous flux with
the lamp life
Luminous To what extend a Hv lxs or lxh
required illuminance is 𝐸𝐸𝑣𝑣 = � 𝐸𝐸(𝑡𝑡) 𝑑𝑑𝑑𝑑
exposure achieved over a ∆𝑡𝑡
period of time
Point source – a light source can be regarded as a point source if the observation distance is
more than 5 times the greatest dimension of the light source
Luminance vs. Illumiannce
→ For completely diffusing surfaces, the luminance is approx. related to illuminance and
𝝆𝝆∙𝑬𝑬
reflectance by: 𝑳𝑳 =
𝝅𝝅
Luminance vs. brightness – The term brightness is a psychophysical quantity and not a photometric
one (while the luminance is impacting the brightness, the luminance is not equal to brightness) – the
functional relation between luminance and brightness is non-linear
, Surface Properties – light interaction with surfaces is characterized by three properties:
ϕ𝜌𝜌
→ Luminous reflectance (ρ): Proportion of light reflected – 𝜌𝜌 =
𝜙𝜙
ϕ𝜏𝜏
→ Luminous transmittance (τ): Proportion of light transmitted – 𝜏𝜏 = 𝜙𝜙
ϕ𝛼𝛼
→ Luminous absorptance (α): Proportion of light absorbed – 𝛼𝛼 =
𝜙𝜙
o These properties always sum to 1: ρ + τ + α = 1
The Inverse Square Law – the illuminance from a point source decreases with the square of the
1 𝑰𝑰
distance – 𝐸𝐸 ∝ → 𝑬𝑬 = – this means that:
𝑟𝑟 2 𝒓𝒓𝟐𝟐
→ Light gets weaker the further you go from its source
o If you double the distance, the illuminance becomes ¼
o If you triple the distance, the illuminance becomes 1/9
→ E.g. how a flashlight beam gets weaker as you point it at things further away
Lambert’s Cosine Law – illuminance on a surface depends on the angle at which light strikes it –
𝑰𝑰𝜶𝜶 ∙𝒄𝒄𝒄𝒄𝒄𝒄 𝜶𝜶
𝑬𝑬 = (α = angle between light direction and surface normal)
𝒓𝒓𝟐𝟐
→ Light falling on a tilted surface spreads out more, making it dimmer
→ E.g. how sunlight is stronger at noon (directly overhead) than at sunset (coming in at an
angle)
Point method – used to calculate the illuminance produced by a luminaire to an individual point
𝑰𝑰𝜶𝜶 ∙ 𝒄𝒄𝒄𝒄𝒄𝒄𝟑𝟑 𝜶𝜶
→ Horizontal illuminance: 𝑬𝑬𝒉𝒉 =
𝒉𝒉𝟐𝟐
o Important!! for reading at a desk, working in the kitchen,
walking on a floor
𝑰𝑰𝜶𝜶 ∙ 𝒄𝒄𝒄𝒄𝒄𝒄𝟐𝟐 𝜶𝜶∙𝒔𝒔𝒔𝒔𝒔𝒔 𝜶𝜶
→ Vertical illuminance: 𝑬𝑬𝒗𝒗 =
𝒉𝒉𝟐𝟐
o Important!! for lighting artwork on walls, illuminating billboards,
making sure faces are well-lit for security cameras
Practice questions CANVAS
1. Suppose a blue and red paper look equally bright under daylight. Explain what
happens when the light is dimmed to moonlight levels.
a. The blue paper looks brighter than the red paper, because rods are more
sensitive to blue than the cones.
b. The red paper looks brighter than the blue paper, because cones are more
sensitive to red.
c. Because of the Purkinje shift, the luminous sensitivity shifts to short
wavelengths making red look lighter than blue in scotopic lighting.
d. The V(λ) curve has more or less the same value for red and blue light, so
the papers look equally bright.
2. The efficacy of light sources is expressed in
a. lm
b. lm/W
c. W
d. %
3. Which of the following is correct:
Chapter 1 – Photometry (5Q)
Summary information
Light is a form of electromagnetic radiation with wavelengths between 380 nm (violet) and 780
nm (red).
The visible spectrum includes:
Violet (380-420 nm) Green (495-566 nm) Red (627-780 nm)
Indigo (420-450 nm) Yellow (566-589 nm)
Blue (450-495 nm) Orange (589-627 nm)
Beyond visible light:
→ Infrared (longer wavelength, felt as heat)
→ Ultraviolet (shorter wavelength, can damage skin/eyes)
Photometry = the science of measuring light according to human eye sensitivity functions (CIE –
International Commission on Illumination)
→ Unlike radiometry (which measures all electromagnetic radiation), photometry specifically
focuses on visible light and how humans perceive it
The retina contains specialized cells called photoreceptors that convert light into neural signals.
There are two main types of photoreceptors:
→ Cones (~5 million): Active in higher light levels, responsible for color perception. – photopic
vision (daylight)
o L-cones: Sensitive to long wavelengths (564 nm) – red
o M-cones: Sensitive to medium wavelengths (534 nm) – green
o S-cones: Sensitive to short wavelengths (420 nm) – blue
→ Rods (~110 million): Active in low light conditions, highly sensitive to brightness but not
color – cannot distinguish colors – scotopic vision (night vision)
Spectral Sensitivity – the human eye's sensitivity varies with wavelength:
→ Peak sensitivity at 555 nm for photopic vision (daylight, cones) – GY – V(λ) function
→ Peak sensitivity at 507 nm for scotopic vision (night vision, rods) – BG – V’(λ) function
→ 540×1012 Hz is the frequency of green light
Quantity Definition Symbol Unit Formula
Luminous Total amount of light Фv lm (lumen) 𝑄𝑄𝑣𝑣
𝜙𝜙𝑣𝑣 =
emitted by a source in
flux all directions 𝑡𝑡
𝜙𝜙𝑣𝑣 = 𝐾𝐾𝑚𝑚 ∙ � 𝜙𝜙𝑒𝑒,𝜆𝜆 ∙ 𝑉𝑉(𝜆𝜆) ∙ ∆𝜆𝜆
𝐾𝐾𝑚𝑚 = max. photometric equivalent of
radiation = 683 lm/W
𝜙𝜙𝑒𝑒 = radiant flux (mW/nm)
Luminous Amount of light Iv cd 𝐼𝐼𝑣𝑣 =
𝜙𝜙𝑣𝑣
emitted in a specific
intensity direction
(candela) = Ω
lm/sr Ω = solid angle (sr – steradians)
𝐴𝐴
Ω= a full sphere: 4π sr
𝑟𝑟 2
, Luminous Different light sources η lm/W 𝜂𝜂 =
𝜙𝜙𝑣𝑣
convert electrical
efficacy power to light with 𝑃𝑃
- 10 lm/W – incandescent lamp
varying efficiencies
- 60 lm/W compact fluorescent lamp
(indicator for energy
(CFL)
efficiency of a lamp)
- 150 lm/w LED lamp – can exceed
𝐾𝐾𝑚𝑚 = max. luminous efficacy of
radiation = 683 lm/W
Illuminance Amount of light Ev lx (lux) = 𝐸𝐸𝑣𝑣 =
𝜙𝜙𝑣𝑣
falling on a surface - Ehor – measured on lm/m2 𝐴𝐴
horizontal surfaces (desk) 𝐴𝐴 = area
– important in general
tasks (reading)
- Ever – measured on
vertical surfaces (walls) –
important in sports field
Luminance Perceived brightness Lv cd/m2 𝐼𝐼𝑣𝑣
of a surface 𝐿𝐿𝑣𝑣 =
𝐴𝐴𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
𝐴𝐴𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝐴𝐴 ∙ cos (𝜀𝜀1 )
Luminous Total amount of light Qv lms or
that a lamp can 𝑄𝑄𝑣𝑣 = � 𝜙𝜙(𝑡𝑡) 𝑑𝑑𝑑𝑑
energy produce over its lmh ∆𝑡𝑡
lifetime by weighing
its luminous flux with
the lamp life
Luminous To what extend a Hv lxs or lxh
required illuminance is 𝐸𝐸𝑣𝑣 = � 𝐸𝐸(𝑡𝑡) 𝑑𝑑𝑑𝑑
exposure achieved over a ∆𝑡𝑡
period of time
Point source – a light source can be regarded as a point source if the observation distance is
more than 5 times the greatest dimension of the light source
Luminance vs. Illumiannce
→ For completely diffusing surfaces, the luminance is approx. related to illuminance and
𝝆𝝆∙𝑬𝑬
reflectance by: 𝑳𝑳 =
𝝅𝝅
Luminance vs. brightness – The term brightness is a psychophysical quantity and not a photometric
one (while the luminance is impacting the brightness, the luminance is not equal to brightness) – the
functional relation between luminance and brightness is non-linear
, Surface Properties – light interaction with surfaces is characterized by three properties:
ϕ𝜌𝜌
→ Luminous reflectance (ρ): Proportion of light reflected – 𝜌𝜌 =
𝜙𝜙
ϕ𝜏𝜏
→ Luminous transmittance (τ): Proportion of light transmitted – 𝜏𝜏 = 𝜙𝜙
ϕ𝛼𝛼
→ Luminous absorptance (α): Proportion of light absorbed – 𝛼𝛼 =
𝜙𝜙
o These properties always sum to 1: ρ + τ + α = 1
The Inverse Square Law – the illuminance from a point source decreases with the square of the
1 𝑰𝑰
distance – 𝐸𝐸 ∝ → 𝑬𝑬 = – this means that:
𝑟𝑟 2 𝒓𝒓𝟐𝟐
→ Light gets weaker the further you go from its source
o If you double the distance, the illuminance becomes ¼
o If you triple the distance, the illuminance becomes 1/9
→ E.g. how a flashlight beam gets weaker as you point it at things further away
Lambert’s Cosine Law – illuminance on a surface depends on the angle at which light strikes it –
𝑰𝑰𝜶𝜶 ∙𝒄𝒄𝒄𝒄𝒄𝒄 𝜶𝜶
𝑬𝑬 = (α = angle between light direction and surface normal)
𝒓𝒓𝟐𝟐
→ Light falling on a tilted surface spreads out more, making it dimmer
→ E.g. how sunlight is stronger at noon (directly overhead) than at sunset (coming in at an
angle)
Point method – used to calculate the illuminance produced by a luminaire to an individual point
𝑰𝑰𝜶𝜶 ∙ 𝒄𝒄𝒄𝒄𝒄𝒄𝟑𝟑 𝜶𝜶
→ Horizontal illuminance: 𝑬𝑬𝒉𝒉 =
𝒉𝒉𝟐𝟐
o Important!! for reading at a desk, working in the kitchen,
walking on a floor
𝑰𝑰𝜶𝜶 ∙ 𝒄𝒄𝒄𝒄𝒄𝒄𝟐𝟐 𝜶𝜶∙𝒔𝒔𝒔𝒔𝒔𝒔 𝜶𝜶
→ Vertical illuminance: 𝑬𝑬𝒗𝒗 =
𝒉𝒉𝟐𝟐
o Important!! for lighting artwork on walls, illuminating billboards,
making sure faces are well-lit for security cameras
Practice questions CANVAS
1. Suppose a blue and red paper look equally bright under daylight. Explain what
happens when the light is dimmed to moonlight levels.
a. The blue paper looks brighter than the red paper, because rods are more
sensitive to blue than the cones.
b. The red paper looks brighter than the blue paper, because cones are more
sensitive to red.
c. Because of the Purkinje shift, the luminous sensitivity shifts to short
wavelengths making red look lighter than blue in scotopic lighting.
d. The V(λ) curve has more or less the same value for red and blue light, so
the papers look equally bright.
2. The efficacy of light sources is expressed in
a. lm
b. lm/W
c. W
d. %
3. Which of the following is correct:
