Chapter 26 - Physics Notes

Intensity: The brightness of a light source, measured in candelas (cd).
Luminous Flux (Φ): The total amount of light that a source gives off, measured in lumens (lm).
Illuminance (E): The amount of light an object receives from a light source, measured in lux (lx).
Transmittance: The ratio of the transmitted luminous flux to the incident flux.
Color: The perception of different frequencies of light, which can be received directly from a source, by reflection from a surface, or by transmission through a material.

Intensity

Intensity is the luminous intensity of a source that emits monochromatic radiation of frequency 540 × 10¹² Hz with a radiant intensity of 1/683 watt per steradian.
A steradian is a conical solid angle with its vertex at the center of a sphere that cuts off a circular area on the surface of the sphere equal to the square of the sphere’s radius.
A high-wattage light bulb uses its power more efficiently than a low-wattage bulb.
Luminance is the rate of flow of light energy reaching a surface in a given direction from the source, measured in cd/m².

Luminous Flux

Luminous flux (Φ) is the total amount of light that a source gives off, measured in lumens (lm).
1 lumen is the luminous flux of a 1 cd light source in 1 steradian.
A 1 cd point light source has a total luminous flux of 4π ≈ 12.57 lm.
Luminous flux and luminous intensity are both measures of power.

Illuminance

Illuminance (E) is the amount of light an object receives from a light source, measured in lux (lx).
Illuminance is directly proportional to luminous flux and inversely proportional to the square of the distance from the source: E = Φ / r².

Example: Calculating Illuminance

What is the illuminance 5.0 m from a point source emitting 975 lm?

r = 5.0 m

Φ = 975 lm

E = Φ / (4πr²)

E = 975 lm / (4π(5.0 m)²)

E = 3.1 lx

Example: Determining Luminous Intensity

What is the luminous intensity of a light source if it produces an illuminance of 85.0 lx at a distance of 1.50 m?

E = 85.0 lx

r = 1.50 m

I_v = E × r²

I_v = (85.0 lx) × (1.50 m)²

I_v = 191 cd

Example: Finding Distance

Your normal desk lamp has a standard 100.0 cd bulb and sits 78.0 cm away from your desk. The bulb burns out, and you have only a 61.0 cd bulb to replace it. How far from your desk will you need to place your lamp with the new bulb to have the same illuminance?

I_v1 = 100.0 cd

I_v2 = 61.0 cd

r₁ = 78.0 cm

r₂ = ?

E₁ = E₂

I_v1 / r₁² = I_v2 / r₂²

r₂ = r₁ √(I_v2 / I_v1)

r₂ = 78.0 cm √(61.0 cd / 100.0 cd)

r₂ = 60.9 cm

Transmittance

Transmittance is the ratio of the transmitted luminous flux to the incident flux.
Transparent materials allow most light through, allowing us to see clearly through them.
Translucent materials transmit light but distort it so that we cannot see clearly through them.
Opaque materials do not transmit visible light.

Color

Color is the perception of different frequencies of light, which can be received directly from a source, by reflection from a surface, or by transmission through a material.
The light’s frequency is related to the energy change of the electrons by the equation E = hf, where f is the frequency and h is Planck’s constant (6.626 × 10^–34 J·s).
Color appearance is affected by hue, saturation, and brightness.
An object’s color also depends on the colors of surrounding objects.

Additive Color Mixing

The additive primary colors are red, green, and blue.
Combinations of these three colored lights can produce any color in the spectrum.
No combination of additive primary colors can produce black; only the total absence of light is perceived as black.

Colored Objects

A red object appears red because the light coming from it to your eyes is red.
Three reasons why the light might be red:
- It may be illuminated only by red light.
- It may reflect only red light (absorbs all other colors).
- If not opaque, it may transmit only red and absorb all other colors.
Pigment: the substance in an object that absorbs certain colors and reflects others.

Subtractive Color Mixing

The subtractive primary colors are cyan, magenta, and yellow.
This governs the color of reflected light, since some colors will be absorbed and others will not.
No mixture of the subtractive primary colors can produce white light.

Questions for Students

Define intensity and its unit of measurement.
Explain the concept of luminous flux and how it is measured.
Describe the relationship between illuminance and distance from a light source.
What is transmittance and how does it differ between transparent, translucent, and opaque materials?
Explain additive and subtractive color mixing and provide examples.

Chapter 26: Using Light

26.A: Intensity and Color