Physics
Photometry
Vision and Brightness
11
⚡ Quick Summary
We see objects because light from them enters our eyes. The brightness we perceive depends on the amount and wavelength of light energy.
N/A
- An object is visible when light coming from it enters our eyes and stimulates vision.
- The brightness we perceive is determined by:
- The amount of light energy entering the eye.
- The wavelength distribution of the light energy.
Total Radiant Flux
11
⚡ Quick Summary
Total radiant flux is the total energy radiated by a source per unit time, encompassing all wavelengths.
N/A
- Total Radiant Flux: The total energy of radiation emitted by a source per unit time.
- Includes radiation components of various wavelengths, even beyond the visible range.
- Calculated by summing the energy emitted per unit time across all wavelengths.
- SI unit: Watt (W)
Luminosity of Radiant Flux
11
⚡ Quick Summary
Luminosity measures the capacity of radiation to produce a brightness sensation. It depends on both the radiant flux and the wavelength.
N/A
- Luminosity of Radiant Flux: A measure of the capacity of radiation to produce a brightness sensation in the eye.
- Brightness depends on the wavelength of the radiation and the total radiant flux.
- Example: A 10W yellow light source appears brighter than a 10W red light source.
Luminous Flux and Relative Luminosity
11
⚡ Quick Summary
Luminous flux represents the total brightness producing capacity of a source, measured in lumens. Relative luminosity compares the brightness produced by different wavelengths relative to 555 nm.
Relative luminosity = (luminous flux of a source of given wavelength) / (luminous flux of a 555 nm source of same power)
- Luminous Flux: A quantity directly representing the total brightness producing capacity of a source. It differs from radiant flux by accounting for the eye's sensitivity to different wavelengths.
- Unit: Lumen (lm).
- Definition of Lumen: The luminous flux of a source of 1/685 W emitting monochromatic light of wavelength 555 nm is one lumen. This implies a 1 W source emitting monochromatic light of 555 nm emits 685 lumens.
- Relative Luminosity: A fraction representing the luminous flux of a given wavelength relative to the luminous flux of a 555 nm source of the same power.
- Figure 22.1 shows relative luminosity as a function of wavelength under normal light conditions. The luminosity is maximum around 555 nm and decreases on either side.
- Radiation is considered "visible" if its luminosity is not zero.
- Luminous flux depends on both radiant flux and wavelength distribution.
Illuminance
11-12
⚡ Quick Summary
Illuminance is the amount of light falling on a surface area. It's measured in lux (lumens per square meter) and directly relates to how bright the area appears.
['E = dF/dA']
Illuminance (E) is defined as the luminous flux (dF) incident per unit area (dA). It is directly related to the brightness of an illuminated area. The SI unit of illuminance is lumen/m², also known as lux.
Inverse Square Law
11-12
⚡ Quick Summary
The brightness of light decreases as you move farther from the source. The illuminance is inversely proportional to the square of the distance from the light source and also depends on the angle at which light strikes the surface.
['E = (I cosθ) / r²']
The illuminance (E) at a small area dA due to a point source with luminous intensity I at a distance r, where the angle between the normal to the area and the direction to the source is θ, is given by E = (I cosθ) / r². This demonstrates the inverse square law and the dependence on the angle of incidence.
Lambert's Cosine Law
11-12
⚡ Quick Summary
Lambert's cosine law describes how the intensity of light emitted from a perfectly diffused surface varies with the angle. The intensity is maximum along the normal and decreases as the angle increases.
['I = I₀ cosθ']
For perfectly diffused surfaces, the luminous intensity (I) in a direction making an angle θ with the normal is given by I = I₀ cosθ, where I₀ is the luminous intensity along the normal.
Photometers
11-12
⚡ Quick Summary
Photometers are instruments used to compare the intensities of two light sources by adjusting distances until two screens appear equally bright. The intensities are then related to the square of the distances.
['I1/d1² = I2/d2² or I1/I2 = d1²/d2²']
Photometers compare the intensities of two point sources by illuminating two screens side by side. By adjusting the distances (d1 and d2) of the sources (S1 and S2) until the screens appear equally bright, the intensities (I1 and I2) can be compared using the relationship I1/d1² = I2/d2².
Illuminance Comparison
XI
⚡ Quick Summary
Two light sources' intensities can be compared by adjusting their distances from a central spot until they provide equal illuminance. By measuring these distances, the ratio of their intensities can be determined.
I1 / d1^2 = I2 / d2^2 => I1 / I2 = (d1 / d2)^2
A grease spot photometer is used. Two light sources S1 and S2 are positioned on either side of a central stand with a white paper containing a grease spot. Plane mirrors M1 and M2 behind the stand allow simultaneous viewing of the grease spot's images. The distances d1 and d2 of the sources from the spot are adjusted until the illuminance from both sources appears equal. At this point, the intensities I1 and I2 of the sources are related by the equation I1/I2 = (d1/d2)^2.
Radiant Flux
XI
⚡ Quick Summary
Radiant flux is the total energy radiated by a source per unit time, measured in Watts (W).
Radiant Flux = Total energy radiated per unit time (W)
Total radiant flux is equivalent to the total energy radiated per unit time, expressed in Joules per second (J/s) or Watts (W). It considers the energy of light at all wavelengths emitted by the source.
Luminous Flux
XI
⚡ Quick Summary
Luminous flux measures the perceived brightness of light, weighted by human eye sensitivity, and is measured in lumens.
Luminous Flux (lumens) = Radiant Flux (Watts) * Luminous Efficacy (lumens/Watt)
Luminous flux is a measure of the total amount of visible light emitted by a source, taking into account the varying sensitivity of the human eye to different wavelengths. It is calculated by weighting the radiant flux at each wavelength by the luminous efficiency function, which represents the relative sensitivity of the eye. The unit of luminous flux is the lumen (lm).
Luminous Efficiency
XI
⚡ Quick Summary
Luminous efficiency is the ratio of total luminous flux to total radiant flux, measuring how effectively a source converts energy into visible light.
Luminous Efficiency = Total Luminous Flux / Total Radiant Flux (lumens/Watt)
Luminous efficiency is defined as the ratio of the total luminous flux (in lumens) to the total radiant flux (in Watts). It represents the effectiveness of a light source in converting electrical power into visible light.
Luminous Intensity
XI
⚡ Quick Summary
Luminous intensity measures the amount of light emitted by a source per unit solid angle in a specific direction, quantified in candelas.
I = dF/dw, where I is luminous intensity, dF is luminous flux, and dw is the solid angle
Luminous intensity (I) is a measure of the luminous flux emitted per unit solid angle in a specific direction. It is measured in candelas (cd), where 1 candela is equal to 1 lumen per steradian (lm/sr).
Solid Angle
XI
⚡ Quick Summary
Solid angle measures how large an object appears from a point, expressed in steradians.
w = Area / r^2
The solid angle (ω) subtended by an area at a point is defined as the area projected onto a sphere of unit radius centered at that point. It is measured in steradians (sr). For a small area dA at a distance r, where r is much larger than the dimensions of dA and the area is perpendicular to the line of sight, the solid angle is approximately dA/r^2.
Luminous Flux and Solid Angle
XI
⚡ Quick Summary
Luminous flux relates to luminous intensity through the solid angle it covers.
ΔF = I * Δω
Luminous flux emitted into a solid angle is equal to the product of luminous intensity and the solid angle: ΔF = I * Δω, where ΔF is the luminous flux, I is the luminous intensity, and Δω is the solid angle.
Illuminance and Luminous Intensity
XII
⚡ Quick Summary
Photometry deals with the measurement of light, specifically luminous flux and illuminance. Luminous intensity describes the power emitted by a light source in a particular direction, while illuminance describes the amount of light falling on a surface.
['I = F / (4π) (for a uniform point source)', 'E = I cos(θ) / r²', "I = I₀ cos(θ) (Lambert's Cosine Law)"]
- Luminous Flux (F): The total amount of light emitted by a source, measured in lumens.
- Luminous Intensity (I): The luminous flux emitted per unit solid angle, measured in candela (cd). I = F / (4π) for a source emitting uniformly in all directions.
- Illuminance (E): The luminous flux received per unit area of a surface, measured in lux. E = I cos(θ) / r², where I is the luminous intensity, r is the distance from the source to the surface, and θ is the angle between the normal to the surface and the direction of the light.
- Lambert's Cosine Law: The luminous intensity (I) of a perfectly diffused source varies with the cosine of the angle (θ) between the viewing direction and the normal to the surface: I = I₀ cos(θ), where I₀ is the intensity along the forward normal.
Brightness of a Light Source
11
⚡ Quick Summary
The brightness of a light source as perceived by the eye depends on the amount of light energy entering the eye per second, also known as the luminous flux. The wavelength also plays a key role, as the eye is more sensitive to certain wavelengths (around 555 nm).
No formulas explicitly mentioned in the text.
- Luminous Flux: The total luminous flux entering the eye determines the brightness sensed.
- Wavelength Dependence: The eye's sensitivity varies with wavelength, with maximum sensitivity around 555 nm.
- Illuminance: Illuminance is the luminous flux received per unit area.
Illuminance and Distance
11
⚡ Quick Summary
Illuminance decreases as the distance from the light source increases. For a point source, illuminance is inversely proportional to the square of the distance. For a long cylindrical source, the intensity is inversely proportional to the distance.
I ∝ 1/r<sup>2</sup> (point source), I ∝ 1/r (cylindrical source)
- Point Source: Illuminance (I) ∝ 1/r2, where r is the distance from the source.
- Cylindrical Source: Intensity (I) ∝ 1/r, where r is the distance from the source.
Exposure and Rotation of Light Source
11
⚡ Quick Summary
Exposure is related to the intensity of the light source. Rotating a light source changes the effective area emitting light and thus the required exposure time.
No formulas explicitly mentioned in the text.
When a circular disc source is rotated, the effective area decreases, therefore, the exposure time needs to be adjusted to receive the same amount of light.
Luminous Efficiency
11
⚡ Quick Summary
Luminous efficiency differs between monochromatic and white light sources, and monochromatic sources at specific wavelengths like 555 nm can have higher luminous efficiency.
No formulas explicitly mentioned in the text.
- Monochromatic vs. White Light: The luminous efficiency depends on the type of light source.
- Wavelength Matters: Monochromatic sources at wavelengths near 555 nm have high luminous efficiency.
Radiant Flux vs Luminous Flux
11
⚡ Quick Summary
Radiant flux represents the total energy emitted, while luminous flux represents the visible light energy. Power and radiant flux have the same dimensions, and relative luminosity is dimensionless.
No formulas explicitly mentioned in the text.
- Radiant Flux: Total energy emitted per unit time.
- Luminous Flux: Measure of the perceived brightness of light.
- Power and Radiant Flux: Have the same dimensions.
- Relative Luminosity: Dimensionless quantity.
Radiant Flux
11-12
⚡ Quick Summary
Radiant flux is the rate at which energy is emitted from a source.
Radiant Flux (Φ) = Energy (Q) / Time (t)
Radiant flux is the total amount of radiant energy emitted per unit time, measured in watts (W).
Illuminance
11-12
⚡ Quick Summary
Illuminance is the amount of light falling on a surface.
Illuminance (E) = Luminous Flux (F) / Area (A)
Illuminance (E) is the luminous flux per unit area, measured in lux (lx) or lumen per square meter (lm/m²). It quantifies the amount of light incident on a surface.
Relative Luminosity
11-12
⚡ Quick Summary
Relative luminosity describes the human eye's sensitivity to different colors of light.
N/A (Relative, based on a standardized curve)
The relative luminosity (V(λ)) is a measure of the eye's sensitivity to different wavelengths of light. It is highest at 555 nm (green light).
Luminous Flux
11-12
⚡ Quick Summary
Luminous flux measures the perceived brightness of light.
N/A (Depends on radiant flux and relative luminosity)
Luminous flux (F) measures the total amount of visible light emitted by a source, weighted by the human eye's sensitivity to different wavelengths. It is measured in lumens (lm).
Luminous Efficiency
11-12
⚡ Quick Summary
Luminous efficiency tells you how well a light source converts power into visible light.
Luminous Efficiency = Luminous Flux / Radiant Flux (or Electric Power)
Luminous efficiency is the ratio of luminous flux to radiant flux or electric power consumed, indicating how efficiently a light source converts energy into visible light. Measured in lumen/Watt
Luminous Intensity
11-12
⚡ Quick Summary
Luminous intensity measures the brightness of a light source in a specific direction.
Luminous Intensity (I) = Luminous Flux (F) / Solid Angle (Ω)
Luminous intensity (I) is the luminous flux emitted per unit solid angle in a specific direction. It is measured in candelas (cd).