Physics 1230 Light and Color : Exam #3 Your Last Name Your First & Middle Name General information: This exam will be worth 100 points. There are 15 multiple choice questions worth 3 points each (part 1 of the exam) and problems worth a total of 55 points (part 2 of the exam). There will be no partial credit for the multiple choice problems. Your answers to the problems should be on the same pages as the exam assignment in the provided space (you can use the reverse sides of the pages if you need more space and for calculations). Rules for the exam: The exam will be held during a regular class period. All exam solutions need to be turned in by 5PM. You can use a calculator and a single 8.5 x 11 sheet of paper with equations or notes. The paper must have your name and student number on the top of both sides; the rest of the sheet may be in any format that you choose. If you are eligible for special considerations because of a disability, you must bring a letter from the CU Office of Disability Services. The letter will be in effect for the entire term, and you need submit it only once before the first exam. I will make special arrangements on a case- by- case basis. You may be excused from an exam because of a medical problem; please give me a note from a doctor in this case if possible. I will deal with these situations on a case- by- case basis. The exam solutions will be posted at http://www.colorado.edu/physics/phys1230/phys1230_fa11/exams.htm soon after the exam. The exam scores will be posted at https://culearn.colorado.edu Useful information: Relationship between frequency and wavelength of light: λ ν = c λ = wavelength, ν = frequency, c = speed of light (3 x 10 8 m/s in empty space). Chromaticity diagram: "wiring" of chromatic channels Polarized vs. unpolarized light
Visible spectrum of light: Exam Assignment, Part 1 (multiple choice problems, 45 points total): 1.1. Combinations of only red and blue () produce colors that are complementary to yellow () produce colors that are complementary to orange *() produce colors that are complementary to green () produce colors that are complementary to magenta () produce colors that are complementary to cyan 1.2. The saturation of a color specifies () its wavelength () its brightness as perceived by the eye () the amount of black ink needed to print the color () the maximum value of the plot of its intensity as a function of wavelength *() the width of the plot of its intensity as a function of wavelength 1.3. The hue of a combination of two monochromatic lights with wavelengths of 590 nm and 550 nm is () red *() yellow () orange () green () blue
1.4. To print text that is to appear red when viewed in white light, you would use () an ink that absorbs only magenta () an ink that absorbs only yellow () an ink that absorbs only green () an ink that absorbs only blue *() an ink that absorbs only cyan 1.5. A filter that passes only monochromatic red light at 650 nm is placed on top of a filter that passes only monochromatic green light at 530 nm. When 460 nm blue light strikes one side of the pair of filters, the light that comes out of the other side (after passing through both filters) is () red () green () blue () yellow *() black no light comes out the other side 1.6. Light of 350 nm wavelength is combined with light of 750 nm wavelength. For a human with normal vision, this combination appears *() black () red () blue () magenta () white 1.7. If you see two monochromatic lights which have exactly the same output powers and whose wavelengths are 410 nm and 420 nm, then (a) the intensities look the same but the 420 nm light looks greener (b) the intensities and the hues both look the same (c) the 410 nm light appears brighter and the hues look the same
*(d) the 420 nm light appears brighter and the hues look the same (e) the 420 nm light looks brighter and greener In answering this and following question, you may find the following two figures helpful. They are taken from the textbook. The first is figure 9.11 on page 245 and the second is figure 10.5 on page 273. The figure on the left shows the response of the three types of cones in the eye and the figure on the right shows how colors are combined: 1.8. The hue of a combination of two monochromatic lights with colors of 650 nm and 570 nm is (a) red *(b) orange (c) yellow (d) green (e) blue 1.9. In addition to the 3 subtractive primaries, 4 color printing also uses black ink because the 3 subtractive primaries (a) used together produce magenta (b) produce a color that depends on the order they were printed *(c) do not produce a deep enough black when used together (d) used together produce a dark green (e) used together produce a dark blue 1.10. The description of the hue of a color as perceived by the brain is based on
(a) total intensity, red-blue difference and yellow-green difference *(b) total intensity, red-green difference and yellow-blue difference 400 500 600 700 Wavelength (nm) (c) total intensity, red-yellow difference and green-blue difference (d) intensities of yellow, cyan and magenta (e) intensities of red, green and blue 1.11. Combinations of only red and blue (a) produce colors that are complementary to yellow (b) produce colors that are complementary to orange (c) produce light beams that have no well defined color (d) produce light beams that have very low intensity *(e) produce colors that have no corresponding wavelength 1.12. The curve shows the intensity distribution of a light bulb. What do we perceive the color to be? a) Saturated reddish blue b) Red c) Unsaturated magenta d) Unsaturated blue Intensity *e) Unsaturated green 1.13. Refer to the chromaticity diagram on the first page. What colors can you get by additively mixing 580 nm yellow with 480 nm blue of different intensities a) Off white b) Any color c) Any of the colors with a yellowish or bluish look *d) Any of the colors along the line joining the two wavelengths e) Green
1.14. Light coming directly from the Sun through the Earth atmosphere is (a) linearly polarized *(b) unpolarized (c) circularly polarized (d) with linear polarizaqtion state alternating between two orthogonal directions (parallel and perpendicular to horizont) (e) scattered 1.15. The Sky is blue because of (a) Rayleigh scattering of green and red light coming from the Sun (b) additive mixing of colors (c) subtractive mixing of colors (d) a combination of absorption and total internal reflection; * (e) scattering of blue light in the Earth atmosphere. Exam Assignment, Part 2 (55 points total) 2.1. Problems on color mixing and properties of colors (15 points). (a) On the Chromaticity diagram below, show how you can find complementary colors. Explain how one finds complementary colors for red and green using the diagram (5 points). The complement to any wavelength color on the edge of the chromaticity diagram is obtained by drawing a straight line from that color through white to the other edge of the diagram. The lines extended to the opposite edges of the diagram show that the complement to 700 nm red is 490 nm cyan and the complement to green is magenta - a non- wavelength color.
(b) Describe the color shown by a filled circle on the chromaticity diagram below so that people worldwide can understand what color you have in mind (using both words and numbers) and find the dominant hue of this color using the diagram (5 points). Since the chromaticity diagram is a world standard, we can describe this color (greenish yellow) using its chromaticity diagram coordinates: x = 0.4; y = 0.5. To find the dominant hue of the color indicated by the black dot, we draw a straight line from white through the point to get dominant wavelength, and hence, hue (568 nm greenish yellow). This method works because additive mixture of white with a fully- saturated (wavelength) color gives the desaturated color of the original point. (c). Describe how common color printers work; explain what the dots of different size on the image below are intended to represent and how they are related to the color in the squares on the right:
The printers commonly use four inks (cyan, magenta, yellow, and black - CMYK). This image shows 3 examples of color halftoning with CMYK separations. From left to right we see what is printed by the cyan, magenta, yellow, and black inks. Because of color mixing, the combined halftone pattern in the 5 th column will be perceived by the human eye as shown in the 6 th column on the right side. 2.2. Problems on color mixing and properties of colors (15 points total). (a) Using the cone sensitivity graph on 1 st page, determine what color will be perceived by a human eye with normal color vision in the case of light intensity distribution shown below. Explain how you determine this (5 points). The eye will see this light being of white color. Here the eye is viewing a mixture of blue and yellow (e.g., 460 nm blue of intensity 1 and 575 nm yellow of intensity 1.66). The blue light excites mainly s- cones but also a bit of i- cones and a bit of L- cones. The yellow light excites i- cones and (slightly more) L- cones but no s- cones. The result is an equal response of s- cones, i- cones and L- cones, which will be perceived as white color. (b) Using the chromatic channel diagram and cone sensitivity curves below, describe the work of chromatic channels
The 3 kinds of cones are related to r- g and y- b by the way they are connected to neural cells (ganglion cells). Cones of each kind are attached to 3 different neural cells which control the two chromatic channels, y- b and r- g, and the white vs. black channel called the achromatic channel (lightness). When light falls on the L- cones they tell all 3 neural cells to increase the electrical signal they send to the brain. When light falls on the i- cones they tell the r- g channel cell to decrease (inhibit) its signal but tell the other cells to increase their signal. When light falls on the s- cones they tell the y- b channel cell to decrease (inhibit) its signal but tell the other cells to increase their signal. The neural cell for the y- b chromatic channel has its signal inhibited when (blue) light excites the s- cone, INTERPRETED AS BLUE, and enhanced when light excites the i- & L- cones, INTERPRETED AS YELLOW. The neural cell for the r- g chromatic channel has its signal inhibited when (green) light falls on the i- cone INTERPRETED AS GREEN and enhanced when light excites the s and L cone, INTERPRETED AS MAGENTA (Psychological red). The neural cell for the achromatic channel has its signal enhanced when light excites any of the cones (c) Light falling on the center/surround of the receptive fields of the chromatic channels of a human eye with normal is shown below. On each of the 5 cases, mark what color will be perceived/interpreted and explain how double- opponent chromatic channels work. Red Green Green Yellow Yellow R in center and G in the surround both enhance signal (R-G channel ganglion cell signals red) R in surround inhibits the signal (R-G channel ganglion cell signals green) R in surround and G in the center both inhibit signal (R-G channel ganglion cell signals green) Y in center and B in the surround both enhance signal (Y-B channel ganglion cell signals yellow) Y in center enhances signal (Y-B channel ganglion cell signals yellow) 2.3. Questions about light polarization & scattering (10 points). (a). Describe why Sun looks yellow but sunset looks red. (5 points for this problem). The propert of Rayleigh scattering is that the shorter the wavelength, the more light of given wavelength is scattered. For this reason, blue light is scattered much more than red light. One can think of white light from the Sun being a mixture of red, green and blue light. Blue light is scattered the most and does not come to our eyes directly from the Sun. For this reason sun looks yellow (red + green that are left). However, when light travels through even more atmosphere (in the case of Sunset), the light with the next shortest wavelengths (green) is scattered too, so that the Sunset looks red. (b). Assume that light propagates in z-direction and electric field of the propagating electromagnetic wave is shown by blue arrows below. What is the linear polarization direction? Is it possible to extinct this light using a linear polarizer (5 points for this problem).
The linear polarization of this light wave is along the y-direction. Yes, this light can be extinct by an x-polarized linear polarizer. 2.4. Problems involving material of chapters 9, 10, 11, and 13 (15 points total). (a) Mark the Intensity vs. wavelength distribution corresponding to a monochromatic laser source. In a dark room in which you have only one of these light sources, light of what source will not pass through a very good blue color filter? Explain why. (5 points for this problem). Laser A blue color filter adsorbs all visible light except for blue light. The intensity vs. wavelength distribution for the red laser (figure on the left above) is such that there is essentially no light emitted within the spectral range of transmission of a blue color filter. Because of this, this laser beam will be blocked by the blue color filter. In the case of the two other light sources, some light will go through the blue color filter. (b). Describe how one obtains green color when printing photos using a conventional color printer with yellow, cyan, magenta, and black cartridges. (5 points for this problem). Predominantly by using cyan and yellow inks (with possible addition of black if dark green). The inks are printed in the form of dots separated by small distances of the order of 10-100 microns that cannot be distinguished by human eye without optical instruments like microscopes. (c). Describe how one obtains yellow color in a conventional display having only red, blue and green pixels. (5 points for this problem). Because of additive mixing of colors used in displays, red and green colors in displays can combine to yield yellow color. Since the pixels are of size smaller than what a human eye can resolve without the use of optical instruments such as microscopes, the red and green light from the corresponding indistinguishable pixels mixes to produce yellow color.