Color Mixing Study Guide PDF

12/5/24 Color II: Spectral Curves and Color Perception Day 26: Review Color Mixing Spectral Curves Next up: Color Perception...

12/5/24 Color II: Spectral Curves and Color Perception Day 26: Review Color Mixing Spectral Curves Next up: Color Perception Final Review etc. 1 Selective Transmission/Reflection Some materials absorb certain The color of a transparent object wavelengths of light and reflect others depends on the color of the light it transmits – absorbs the rest We see an object as being the color of light that it reflects – absorbs the rest 2 1  12/5/24 Color Mixing Adding colors of light (start with nothing) Removing colors of light (start with white) Complementary colors are opposites on the color wheel(s) Single color of light that you add to make white Single color of paint that you add to make black 3 Shine white light through two filters to make red: These filters should be: A. Blue and Yellow B. Green and Magenta C. Magenta and Yellow D. Magenta and Cyan E. You cannot make red, it’s a primary color 4 2  12/5/24 If you have red, green, and yellow lights shining on a white screen what color will the screen appear? A. Red B. Green C. Yellow D. White E. Yellow-green (Lime) R What if you block the red light? A. Red G B. Green C. Yellow D. White Y E. Yellow-green (Lime) 5 If you shine cyan light onto a green object, what color will it appear? A. Cyan B. Green C. Blue D. White E. Black If you shine cyan light onto a red object, what color will it appear? A. Cyan B. Red C. Blue D. White E. Black 6 3  12/5/24 Two colored lights (point sources!) are shining at a mask with a pinhole. Light from the sources hits the screen only where it’s not blocked by the mask Creates five disLnct regions on the screen Indicate what color each of the five regions will appear 7 Two colored lights (point sources!) are shining at a hanging object, which will cast a shadow Again, light only hits the screen where it is not blocked Again, have 5 distinct regions on the screen Indicate what color each of the five regions will appear 8 4  12/5/24 These two situations are inverted Same colors, same mixing, but in different regions Pinhole allows light only through the center Object casts a shadow, blocks light through the center 9 Colored Shadows Color comes from light Shadows come from removing light Colored shadows come from removing specific colors of light (and leaving others) 10 5  12/5/24 Spectral Curves Spectral emission How much light of each wavelength is emiTed? 12 Spectral Curves Not just for emitting light Can also have spectral reflection/transmission curves Focus in on the visible What does red light look like? Same spectral curve for anything that looks red Seeing red means not seeing green or blue (or anything else) 13 6  12/5/24 100% 100% intensity intensity 100% An object that reflects light following the spectral curve above would appear: intensity A. Red B. Magenta C. White D. Pink 14 Ink transmission/reflection curves Magenta Cyan Yellow 100% intensity Absorbs Absorbs Absorbs Green Red Blue Each ink color selectively absorbs one wavelength of light, M Y removing it from the light we see. C 15 7  12/5/24 The spectral curve for yellow light could be: A. A peak at yellow and nothing else B. A peak at red and a peak at green C. A peak at red, yellow, and green D. A and B only E. A, B, and C 16 Seeing Yellow Spectral Emission Curves (Light Input to Eyes) Two possibilities: 100% We see pure yellow light intensity (i.e., yellow photons) We see a mix of red and green light 100% intensity Metamers look the same color to us, but have different spectral emission curves 17 8  12/5/24 The spectral curve for magenta light has: A. A peak at magenta and nothing else B. A peak at red and a peak at blue C. A peak at red, blue, and magenta D. A and B only E. A, B, and C 18 So what about Magenta? Spectral emission curve for magenta 100% intensity 19 9  12/5/24 Mixing light The eye does one of two things Average nearby colors to a central value of wavelength that appears to be A spectral color like Yellow + Red = Orange Or Blue + Green = Cyan Averages “distant” colors to something non-spectral Red + Blue = Magenta Orange + Blue = Brown 20 Farmer and the Seeds: Color Mixing Edition Have a model for color addition Spectral colors are different wavelengths of light with different energies, non-spectral colors come from mixing spectral colors Have a theory for color addition Can make all colors (spectral and non-spectral) by mixing (adding) three primary colors of light From experiment, these colors are Red, Green, and Blue The complementary colors (Cyan, Magenta, Yellow) each remove the corresponding primary color of light, leaving two others Mixing pigments/filters of these complements can also lead to any color What’s the interpretation? That is, why is this true? What’s special about RGB light? Our eyeballs are specifically attuned to these three wavelengths 22 10  12/5/24 23 Rods and Cones Rods handle vision in low light Denser on the periphery of the retina. Why you can sometimes see dim things better from the corner of your eye Cones handle color and detail Denser toward the center (fovea) Three different types of cones 24 11  12/5/24 Cones: Red, Green, Blue Each cone responds (most strongly) to different wavelengths Named for the color they are most responsive to (RGB) Short, Intermediate, Long is more accurate, since each cone is sensitive to a range of colors Cells fire either “yes” or “no” to the presence of light 25 When many green photons enter our eye: A. Only the Short cone fires B. Only the Intermediate cone fires C. Only the Long cone fires D. All three cones fire equally E. All three cones fire, but unequally Generally going to say a single photon only activates its corresponding cone Not always true Also, tricky to get individual photons in practice 27 12  12/5/24 When many yellow photons enter our eye: A. Only the Short cone fires B. Only the Intermediate cone fires C. Only the Long cone fires D. The Long and Intermediate cones fire equally E. The Long and Intermediate cones fire unequally Sensitivity curve shows equal sensitive of Intermediate and Long to yellow light Yellow makes both fire 28 Seeing “pure” light Cones fires either “yes” or “no” to the presence of light Our brain turns this signal into percep]on of color A single blue photon will acLvate only the Short (blue) cone A single green photon will acLvate only the Intermediate (green) cone Many green photons will acLvate mostly the Green cone, but some Red and Blue too A single yellow photon can acLvate either Red or Green Many yellow photons acLvate the Red and Green cones equally 29 13  12/5/24 Seeing “mixed” light Cones fires either “yes” or “no” to the presence of light Our brain turns this signal into perception of color Average “nearby” colors to a central value of wavelength (a spectral color) Blue + Green = Cyan Yellow + Red = Orange Averages “distant” colors to something non-spectral Red + Blue = Magenta Orange + Blue = Brown 30 Expanded theory Red, Green, and Blue are the primary colors because they correspond to receptors in our eye How we see color is based on how light interacts with our biology Now not just rote algorithm (says use RGB in this way) Interpretation tells us why this works Eventually, with further testing, becomes integral aspect of theory Also allows us to predict new stuff! For example: why do some people not see color this way? There are several kinds of color vision problems (color “deficiencies”): Wavelength of one kind of cone is shifted One type of cone is missing (R, G, B) Channel wiring is incorrect (R-G, Y-B) 31 14  12/5/24 Several types of color-blindness 32 Deuteranomaly (Red-Green colorblindness) The most common forms of colorblindness Green cone shifted - Red and green light causes more similar response from both the R and G cones Can see both red and green light, but harder to distinguish Red flowers look identical to green leaves 33 15  12/5/24 Final Logistics Final is Thursday 12/12 in NC1005 (normal class) Time is 9:30 AM – 11 AM Structure is the same 80 minutes individual + ~40 minutes group Will post a coversheet Can also bring a crib sheet, just like the prior exams Handwritten One side 8.5x11 NOT “handwritten” meaning zoomed in on a tablet… 34 “Semi-cumulative” with three main units EM Waves Photons, Atoms, and Energy Wave Basics (wavelength, frequency, etc.) Energy of a photon Speed of light, index of refraction Energy of a beam (many photons) Wavelength/frequency in a material Bohr Model Making an EM wave from current/charges Atomic energy levels EM Spectrum Luminescence and absorpLon/emission spectra Blackbody Radiation and Incandescence RelaLng waves and photons Doppler Interference Two slit Peacock feather Cumulative Skills/Prior Content Optics Should not require deep additional studying Color mixing and perception Color Addition and Subtraction Vector addition/cancellation Spectral Curves Difference between a force and a field Rods/Cones Simple Circuits – e.g. resistors in series/parallel 35 16  12/5/24 EM Waves Wave Basics Relate wavelength, frequency, period of waves Make plots of amplitude and wavelength/frequency for various waves Understand EM spectrum and how wavelength relates to frequency/color Relate the direction of the electric/magnetic field in an EM wave to the charge distribution in an antenna Speed of light, index of refraction Determine speed and wavelength of light in various materials Relate speed of light to distance and time Blackbody Radiation and Incandescence Describe mechanism of incandescence and relationship to temperature Interpret spectral curves from BBR, relate to amplitude and wavelength of EM wave Doppler Understand and describe shifts in wavelength/frequency based on motion of the source and/or observer Use the Doppler formula to relate observed/emitted wavelength/frequency and speed Understand effect of 𝑣 < 𝑣! , 𝑣 = 𝑣! , 𝑣 > 𝑣! Sketch wavefront diagrams 36 EM Waves Interference Understand and describe two types of interference (constructive and destructive) both conceptually and mathematically Understand and determine path length difference from geometry for Two slit “thin film” (peacock feather) Understand the meaning of “m” and apply to two slit/thin-film situations Determine changes to an interference pattern (bright/dark spots) on a screen Determine colors reflected, not reflected, weakly reflected from “thin films” Make sketches showing interference of reflected rays 37 17  12/5/24 Photons, Atoms, and Energy Energy of a photon Relate energy of individual photons to color (wavelength/frequency) Describe individual photon interacLons Energy of a beam (many photons) – RelaLng waves and photons Relate energy of a beam to the energy and number of photons Relate amplitude of beam to total energy, number of photons, color of photons, etc. Atomic energy levels Describe absorpLon and emission spectra for atoms Relate absorpLon/emission spectra to energy level diagrams (ELD) Use ELD to determine color/energy of emiaed photons, number of colors of emiaed photons, atomic transiLons, etc. Luminescence and absorpLon/emission spectra Describe mechanism for luminescence Describe spectra of luminescent light and differences from incandescence Describe mulLple kinds of luminescence 38 Optics Color mixing and perception Describe primary colors of (1) light and (2) pigment Determine observed color in various situations (multiple filters, mixing of beams, reflection off colored object, shadows) Draw and interpret spectral reflection/transmission curves Describe observed colors in terms of biological structures in eye (rods/cones) and their activation 39 18  12/5/24 Cumulative Skills/Prior Content Should not require deep additional studying Vector addition/cancellation Given multiple (two) point charges, determine the direction of the net electric field Given the net electric field, determine the relative signs/magnitudes of multiple (two) point charges Given multiple (two) currents, determine the direction of the net magnetic field Given the net magnetic field, determine the relative directions/magnitudes of multiple (two) currents Difference between a force and a field Relate the direction of the electric force 𝐹⃗" on a test charge to the electric field 𝐸 at that location Relate the direction of the magnetic force 𝐹⃗# on a test charge to the magnetic field 𝐵 at that location Determine whether forces (𝐹⃗" / 𝐹⃗# ) or fields (𝐸 / 𝐵) are adding/cancelling Simple Circuits Determine the effect on the total resistance/current when resistors are added or removed in series Determine the effect on the total resistance/current when resistors are added or removed in parallel Determine the fraction of total current in a bulb (e.g. if current will split evenly/unevenly) 40 Structure of test: Content on the test: 15 MC questions Wave basics, Incandescence, Interference, Must do all of them (30 points total) Doppler Many will be “linked” – as in referring to the same situation (3-4 MC, 2 SA) Mix of conceptual and applying expressions Similar to clicker questions in class Photons/Atoms and Beams of light (3-4 MC and 1 SA) 3 short answer questions with one or two parts Must do 2 (10 points total) Optics (color, perception) If you do all 3, I will sum scores - capped at 40 points total (3-4 MC) Must explain your reasoning, may include interpreting and writing expressions (math) Cumulative skills (3-4 MC) Timing: Designed to be ~60 minutes – you have 80 About 2-4 minutes per MC question (~40 minutes) About 10 minutes per SA Turn in exams and form groups of 2-4, repeat the same test One of the SA will become MC 41 19  12/5/24 Electric Force/Field Recap There are two kinds of electric charge (+ and -), opposite charges attract and like charges repel Magnitude of the force (a vector) between two point-charges is given by Coulomb’s Law: 𝑘𝑞!𝑞" 𝐹⃗ = 𝑟" 𝑟 ALL charges make an electric field (a vector) at every point in space. Defined as the force the source charge would exert on another (test) charge if it were placed there: 𝐹⃗ = 𝑞#$%# ' 𝐸 Electric field starts on positive charges and ends on negative charges Electric Force and Electric Field are either in the same or opposite directions 42 Magnetic Force/Field Recap Magnetic fields are made by moving charges (current) Magnetic field made by a steady current wire forms circles given by RHR#1 The strength of the field is 𝜇)𝐼 𝐵&'($ = 2𝜋𝑟 Moving charges in this magnetic field will feel a magnetic force 𝐹⃗* = 𝑞𝑣⃗ × 𝐵 Direction of force is given by RHR#2 Magnetic Force and Magnetic Field are always perpendicular to each other 43 20  12/5/24 Two RHRs RHR#1: Relates the motion of charges (really a current of charges) to the magnetic field these charges create RHR#2: Relates the force that a moving charge (or current of charges) feels to the motion of the charge(s) and the magnetic field that it (they) feels Note that field (𝐵) is always your fingers and velocity/current is always your thumb 𝑣⃗ 𝑣⃗ 44 Reasonable “prior-content” E-field quesDon A proton is fixed in place a distance d to the left of a location in space marked with an “X.” A second charge 𝑞 is going to be placed a distance 2𝑑 to the right of location X, as shown below. For the total (net) electric field at location X to be zero, the charge 𝑞 should be: 𝑑 2𝑑 X Proton Charge 𝑞 A. Positive with the same magnitude of charge as the proton B. Positive with a larger magnitude of charge than the proton C. Negative with the same magnitude of charge as the proton D. Negative with a larger magnitude of charge than the proton E. Something else 45 21  12/5/24 Reasonable “prior-content” circuit question An ideal battery is connected to two identical (Ohmic) bulbs, as shown in the circuit diagram below. Initially the switch is open. When the switch is closed the total current flowing through the battery will: A. Increase B. Decrease C. Remain the same D. Impossible to say without specific values 46 Wave Basics EP Et t x 47 22  12/5/24 AC current (antenna) leads to wiggling electric field. Field at point P changes in time: EP Et t x Field changes in time at specific location Field changes in space at specific time Time between cycles is the period Distance between cycles is the wavelength “wiggliness” is measured by the frequency “wiggliness” is measured by the wavenumber For any wave: 𝑣 = 𝜆𝑓 4𝜋𝑘 𝑚 For EM waves: 𝑐= = 3 5 10% 𝜇$ 𝑠 𝑐 The speed of an EM wave in a material is smaller by n: 𝑣 = 𝑛 48 A wave on a string is moving to the right. The picture at right shows a piece of the string at time 𝑡. 1. What does the vertical axis (amplitude) of this plot show? a) The brightness of the wave b) The energy in the wave c) The maximum displacement (height) of the string d) Both the brightness and the energy, but not the height e) All three of these quantities 2. Which of the following values can be determined from this plot? a) The wavelength b) The frequency c) The speed of the wave d) Both the wavelength and the frequency, but not the speed e) All three of these quantities 49 23  12/5/24 It takes light (an EM wave) a time 𝑡 to travel a distance 𝑑 through air. How long would it take light to move the same distance through glass (𝑛& = 1.5)? A. 𝑡 B. 3𝑡 C. 𝑡/3 D. 2𝑡/3 E. 3𝑡/2 50 “Understanding the relationships between wavelength and frequency isn’t sticking.” EM Waves are made by wiggling charges The frequency of the charge is the frequency of the wave – this defines the wave Can be related to the wavelength: 𝑣 𝑣 = 𝜆𝑓 → 𝜆= 𝑓 3 " 10! 3 " 10" 3 " 10#$ 3 " 10#% 3 " 10$& 3 " 10$! 400 𝑇𝐻𝑧 790 𝑇𝐻𝑧 In vacuum/air (𝒗 = 𝒄) : 750 𝑛𝑚 380 𝑛𝑚 𝟐 In liquid Benzene (𝒗 = 𝒄) : 500 𝑛𝑚 253 𝑛𝑚 𝟑 51 24  12/5/24 Spectral Curves and BBR A spectral curve is a plot of light intensity (brightness) vs. wavelength Shows (1) which color(s) a light is made up of and (2) how much of each color As T goes down: Charges wiggle less/slower Overall brightness goes down Peak frequency goes down Wavelength UP so gets “redder” Peak wavelength given by Wien’s Law: 𝑇𝜆)*+, = 𝑏 = 3 ; 10-. 𝑚 ; 𝐾 BBR gives off a continuous spectrum of colors 52 Photons and Atoms 53 25  12/5/24 Different spectra suggest that light is being made in different ways Incandescence: Continuous spectra, generally from solid objects (metals, sun, you) Depends on Temperature 𝑇𝜆)*+, = 𝑏 = 3 ; 10-. 𝑚 ; 𝐾 Comes from wiggling (free) charges Luminescence: Discrete spectra, generally from gasses (“neon” lights, fire) Depends on type of material Hydrogen, neon, sodium Comes from atomic transitions 54 Light as photons A photon is the smallest possible chunk of light The energy in a photon depends on the color: ℎ𝑐 𝐸?@ABAC = ℎ𝑓 = 𝜆 Bluer is higher energy, redder is lower energy A beam of light is made of many (many!!) photons ℎ𝑐 𝐸B$CD = 𝑁 ' 𝐸E = 𝑁 ' 𝜆 ℎ is Planck’s constant: ℎ = 6.626 " 10'(! 𝐽 " 𝑠 55 26  12/5/24 Bohr Model – Hydrogenic Atoms Any single electron atom follows the Bohr model Radii: 𝑟/ = 𝑛0 𝑎$ ℏ0 𝑟/ = 𝑛0 𝑚* 𝑘𝑍𝑒 0 𝐸$ Energies: 𝐸/ = − 𝑛0 1 𝑚* 𝑘𝑍𝑒 0 0 𝑍0 𝐸/ = − =− 𝐸 𝑛0 2ℏ0 𝑛0 $,2 Allows us to determine the absorption/emission spectra based on the gaps in atomic energy 𝐸) = ∆𝐸+345 = 𝐸6 − 𝐸7 56 The “reddest” (longest wavelength) photon absorbed by Hydrogen has a wavelength 𝜆$. Based on this, what is the energy of the first excited state of Hydrogen? A. 𝜆$ /ℎ𝑐 B. ℎ𝑐/𝜆$ C. 13.6 𝑒𝑉 ; ℎ𝑐/𝜆$ D. 13.6 𝑒𝑉 + ℎ𝑐/𝜆$ E. 𝒉𝒄/𝝀𝟎 − 𝟏𝟑. 𝟔 𝒆𝑽 57 27  12/5/24 The energy level diagram for Hydrogen is shown at right. If you excite a gas of Hydrogen atoms up to their “second excited state”, how many colors of light will be emitted by the gas? A. 1 B. 2 C. 3 D. 4 E. 0 – No colors will be emitted by the gas 58 The energy level diagram for Doubly-Ionized Lithium (which has three protons and one electron) is shown at right. If the longest wavelength photon absorbed by Hydrogen has a wavelength 𝜆$ , then the longest wavelength photon absorbed by ionized-lithium is: A. 𝜆$ B. 3𝜆$ C. 𝜆$ /3 D. 9 𝜆$ E. 𝝀𝟎 /𝟗 59 28  12/5/24 If two beams of light have the same number of photons, then: A. Their amplitudes must be equal B. Their amplitudes could be equal C. Their amplitudes can’t be equal 60 Interference 61 29  12/5/24 What happens when you add two waves? Two extremes might occur (and anything between) 1) The peaks and troughs of both waves line up (we call this being in phase), and thus add up 2) The peaks of one wave line up with the troughs of the other (we call this being out of phase) and thus cancel This is called Interference 62 Wave Interference A defining characteristic of wave behavior is interference Occurs when two waves add together, either get constructive or destructive Constructive: waves add peak to peak, get a bright (loud, tall, etc.) spot Occurs when the two waves are perfectly in phase ∆𝐷9 = 𝑚𝜆 Destructive: waves add peak to trough, get a dark (quiet, small, etc.) spot Occurs when the two waves are perfectly out of phase ; ∆𝐷: = 𝑚 + 𝜆 0 63 30  12/5/24 Many examples of interference. In all cases, consider either constructive or destructive, so the phase difference (“path-length difference”) is ∆𝐷9 or ∆𝐷: Actual Extra Type of = ∆𝐷 = Path Length Interference ? = ∆𝐷 = ? What changes is the specific geometry: Two slit/speaker Thin film/peacock 64 Wave Interference Come up with three unique ways to make the spacing in the pattern smaller A. I’ve got one! B. I’ve got two! C. I’ve got three! D. I’ve got way more than three! 65 31  12/5/24 Peacock Feathers A particular part of the peacock feather has ridges that are 300 nm deep, as shown in the figure. Given that wavelengths of red, orange, green, and blue light are 𝜆< ≈ 700 𝑛𝑚, 𝜆= ≈ 600 𝑛𝑚, 𝜆> ≈ 550 𝑛𝑚, and 𝜆# ≈ 400 𝑛𝑚, what color will this part of the feather not reflect? A. Red 300 𝑛𝑚 B. Orange C. Green D. Blue E. All of these colors will be at least weakly reflected 66 68 32