English: Luminous flux is the measure of the total light power emitted by a light source, and its SI unit is the Lumen.

English: Light brightness (illuminance), measured in lux, is equal to the luminous flux (in lumens) divided by the area (in square meters).

English: Illuminance = Luminous Flux / Area = 1000 lm / 10 m² = 100 lx

English: Luminous flux measures light power within the visible spectrum only, while radiant power measures total electromagnetic energy across all wavelengths.

English: Illuminance is inversely proportional to the square of the distance from the source (inverse square law). When distance doubles, illuminance decreases to one quarter.

English: Luminous intensity is measured in candela (cd) in the SI system, which is the luminous flux per unit solid angle.

English: A sphere has a total solid angle of 4π steradians. Luminous intensity = Luminous flux / Total solid angle = 2000 / (4 × 3.1416) ≈ 159 candela.

English: Atmospheric pressure does not directly affect the apparent brightness of a light source, while other factors like distance, luminous intensity, and light color all affect the visual perception of brightness.

English: Luminous efficacy measures how efficiently energy is converted to visible light (lumens/watt), while radiant efficiency measures how efficiently energy is converted to total electromagnetic radiation (percentage).

English: Luminous flux = Electrical power × Luminous efficacy = 60 watts × 15 lm/W = 900 lumens.

English: We see an object as red because it reflects red light and absorbs other colors of the visible spectrum.

English: The primary colors in the additive (light) color system are Red, Green, and Blue (RGB), which can be combined to produce a wide range of colors.

English: The primary colors in the subtractive (pigment) system are Cyan, Magenta, and Yellow, which form the basis of the CMYK color model used in printing.

English: Mixing red, green, and blue light in equal proportions produces white light, which is the principle behind TV and computer screens.

English: When an object reflects red and green light while absorbing blue light, the combination of red and green produces yellow.

English: The complementary color of blue is yellow, as mixing blue and yellow light produces white light.

English: A rainbow displays spectrum colors due to refraction and dispersion of light inside water droplets, where white light is separated into its constituent colors.

English: The sky appears blue due to Rayleigh scattering, where shorter wavelengths (blue and violet) of sunlight are scattered more in the atmosphere than longer wavelengths.

English: A red filter allows only red light to pass through and absorbs other colors, so only red light will transmit through the filter.

English: Metamerism is a phenomenon where two colors appear to match under one lighting condition but appear different under another, due to differences in their spectral properties.

English: Polarized light is light whose electromagnetic waves vibrate in only one plane, unlike natural light which vibrates in all planes.

English: Malus's law states that the intensity of polarized light passing through a polarizing filter is \[I = I₀ cos²θ\], where θ is the angle between the polarization axis and the direction of vibration of the incident light.

English: When unpolarized light strikes a polarizing filter, the transmitted light intensity is half the original intensity \[(I₀/2),\] regardless of the orientation of the polarization axis.

English: When the axes of two polarizers are parallel, the polarized light from the first passes through the second without additional loss. Final intensity = I₀/2.

English: When the axes of two polarizers are perpendicular, the second filter completely blocks the polarized light from the first. Final intensity = zero.

English: After first filter: I₁ = I₀/2. After second filter (45°): I₂ = I₁ cos²45° = (I₀/2) × (0.5) = I₀/4. After third filter (45° relative to second): I₃ = I₂ cos²45° = (I₀/4) × (0.5) = I₀/8.

English: Brewster's angle is the angle at which light reflects completely plane-polarized, given by\[ tanθ_p = n,\] where n is the refractive index.

English: Light can be polarized by reflection when it reflects at Brewster's angle, resulting in completely plane-polarized reflected light.

English: A common application of polarization is polarized sunglasses that reduce glare reflected from horizontal surfaces like water and roads.

English: Using Malus's law:\[ I = I₀ cos²θ = I₀ cos²60° = I₀ × (0.5)² = I₀ × 0.25 = I₀/4.\]

English: The Doppler effect in light is the change in the observed frequency or wavelength of light due to the relative motion between the light source and the observer.

English: When a light source moves towards a stationary observer, the apparent wavelength decreases (blue shift) because the waves compress in the direction of motion.

English: When a light source moves away from a stationary observer, the apparent frequency decreases (red shift) because the waves stretch in the direction of motion.

English: When a light source moves towards a stationary observer, we use the positive sign: \[ƒ_{obs} = ƒ (1 + v/c),\] where v is the source speed and c is the speed of light.

English: \[ƒ_{obs} = ƒ (1 + v/c) = (5.0 × 10^14) × (1 + 0.1) = (5.0 × 10^14) × 1.1 = 5.5 × 10^14 \;HZ\].

English: When source moves away:\[ Δλ = λ_{obs} - λ = +λv/c.\]\[ λ_{obs} = λ + λv/c = 600 + 600×0.2 = 600 + 120 = 720 nm.\]

English: The redshift amount\[ z = Δλ/λ = v/c = 0.05c/c = 0.05.\]

English:\[Δλ = λv/c → v = c × (Δλ/λ) = c × (100/500) = c × 0.2 = 0.2c.\]

English: The main astronomical application of the Doppler effect is measuring the radial velocity of stars and galaxies by measuring the shift in their spectral lines.

English: Apparent frequency is less than actual frequency, so red shift and source is moving away. \[ƒ_{obs} = ƒ (1 - v/c) → 5.4×10^14 = 6.0×10^14 (1 - v/c) → 0.9 = 1 - v/c → v/c = 0.1 → v = 0.1c.\]