In-depth Exam Notes on Light and Color

Topics for Exam #2: EPS121 – Light and Color

  • Wave Types and Properties

    • Transverse vs. Longitudinal:

    • Transverse Waves: Oscillations are perpendicular to the direction of wave propagation (e.g., light waves).

    • Longitudinal Waves: Oscillations are parallel to the direction of wave propagation (e.g., sound waves).

    • Wave Characteristics:

    • Amplitude: Maximum displacement from equilibrium.

    • Wavelength ($ ext{λ}$): Distance between successive crests or troughs.

    • Frequency ($ ext{f}$): Number of cycles per second (Hz).

    • Period ($ ext{T}$): Time it takes for one cycle ($ ext{T} = 1/ ext{f}$).

    • Wave Speed ($ ext{v}$): Speed at which the wave propagates ($ ext{v} = ext{λf}$).

  • Speed of Light

    • In vacuum: cext=3imes108extm/sext(or187,000miles/sec)c ext{ = } 3 imes 10^8 ext{ m/s} ext{ (or 187,000 miles/sec)}

    • In transparent materials: v=raccnv = rac{c}{n} where nn is the index of refraction.

  • Law of Reflection and Refraction

    • Wave fronts remain continuous across boundaries.

  • Huygen’s Principle

    • Use circular wavefronts to illustrate wave propagation.

  • Electromagnetic Spectrum

    • Typical Wavelength Ranges:

    • Radio: 103extm10^3 ext{ m} to 107extm10^7 ext{ m}

    • Microwaves: 10−2extm10^{-2} ext{ m} to 10−4extm10^{-4} ext{ m}

    • Infrared: 7imes10−7extm7 imes 10^{-7} ext{ m} to 10−3extm10^{-3} ext{ m}

    • Visible: approx. 400extnmextto700extnm400 ext{ nm} ext{ to } 700 ext{ nm}

    • Ultraviolet: 10−8extm10^{-8} ext{ m} to 400extnm400 ext{ nm}

    • X-Ray: 10−11extm10^{-11} ext{ m} to 10−8extm10^{-8} ext{ m}

    • Gamma Ray: Less than 10−11extm10^{-11} ext{ m}

  • Diffraction and Interference

    • Two-slit interference pattern:

    • dextsin(heta)=mextλd ext{ sin}( heta) = m ext{λ} (where dd = distance between slits, hetaheta = angle of the m-th order maximum, mm = order number, extλext{λ} = wavelength).

    • heta=exttan−1(racyR)heta = ext{tan}^{-1}\bigg( rac{y}{R}\bigg), where yy = distance from central maxima and RR = distance to the screen.

  • Human Vision

    • Rods and Cones: Types of photoreceptor cells in the retina responsible for vision under low and bright light, respectively.

    • Color Perception:

    • Primary colors of light: Red, Green, Blue (RGB models).

    • Additive color mixing produces:

      • Yellow (Red + Green)

      • Cyan (Green + Blue)

      • Magenta (Red + Blue)

    • CIE Color Chart: Colors defined by X,Y,ZX,Y,Z where X+Y+Z=1X+Y+Z=1.

    • Purity: extPurity=racextLengthfromWhitetoColorextLengthfromWhitetoPureColorext{Purity} = rac{ ext{Length from White to Color}}{ ext{Length from White to Pure Color}}.

  • Color Filters:

    • Allow certain wavelengths to pass while absorbing others.

    • Example: A magenta filter absorbs green light and passes red and blue light.

  • Subtractive Colors:

    • Primary pigments: Cyan, Magenta, Yellow.

    • Mixing these produces secondary colors while subtracting wavelengths from white light.

  • Color Vision Deficiencies:

    • Protanopia/Protanomaly (Red), Deuteropia/Deuteranomaly (Green), Tritanopia/Tritanomaly (Blue).

  • Polarization of Light:

    • Light can be polarized by reflection or filtering.

    • Malus’s Law: Describes the intensity passing through linear polarizers.

    • Brewster’s Angle: Angle at which reflected light is totally polarized.

  • Electromagnetic Waves:

    • Oscillating electric and magnetic fields, propagating through space without a medium.

    • Right Hand Rule: Determines the direction of wave propagation. For instance, if extEext{E} is along the +z axis and extBext{B} is along the -x axis, the wave propagates along the -y axis.

  • Rainbow Formation:

    • Primary Rainbow: Light enters raindrop, reflects internally, and exits at angles (40° - 42° for violet and red, respectively).

    • Secondary Rainbow: Caused by two internal reflections, appearing lower with reversed color order.

  • Mathematical Relationships:

    • Speed of Sound Example: v=extλfv = ext{λf}

    • Wavelength Calculation: extλ=racvfext{λ} = rac{v}{f}, e.g., for sound with frequency of 850 Hz in air at 343 m/s: extλext=0.403extm,T=0.001176extsext{λ} ext{ = } 0.403 ext{ m}, T = 0.001176 ext{ s}.

By carefully studying these notes, key concepts about light and color, wave properties, and human vision will be more comprehensible and informative for the exam.