Physics 1230 Light and Color : Exam #1 Your full name: Last First & middle General information: This exam will be worth 100 points. There are 10 multiple choice questions worth 5 points each (part 1 of the exam) and problems worth a total of 50 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 the course web page soon after the exam. The exam scores will be posted at https://culearn.colorado.edu Equations: Lens equation 1 f 1 1 + x o x i =, where f is focal length of a lens (positive for convex converging lens), x o is distance from center of lens to object, x i is distance from center of lens to image (positive if on opposite side of lens from object) Magnification equation: M = s i /s o = - x i /x o, where s i = size of image (perpendicular to axis), s 0 = size of the object (in direction perpendicular to the axis) Law of refraction: The amount of light bending at an interface of two media is determined by the law of refraction (the so- called Snell's law): n i sinθ i = n t sinθ t, where θ i = angle between incident ray and normal, θ t = angle between transmitted ray and normal, n i and n t are the indices of refraction in the medium containing the incident ray and in the medium containing the transmitted ray. 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). Critical angle & total internal reflection: n 1 and n 2 are the indices of refraction in the medium containing the incident ray and in the medium containing the transmitted ray, respectively. Bending power of a lens: P = 1/f P = power in diopters, f = focal length of the lens in meters Combined power of two thin lenses in contact: P 1 + P 2 = P P 1 = power of lens 1; P 2 = power of lens 2; P = power of combined lenses
Exam Assignment, Part 1 (multiple choice problems, 50 points total): 1.1. A wavelength of 633 nm is numerically equivalent to (5 points) (*) 0.633 µm and 633 x 10-9 m () 0.633 mm and 63.3 x 10-8 m () 0.0633 m and 633 x 10-4 m () 6.33 mm and 63.3 x 10-5 m () none of the above 1.2. Using the speed of light in vacuum, calculate how long it takes a light signal to travel on a straight line from Denver to New York, a distance of 2,000 km. (5 points) (*) 6.67 x 10-3 s () 0.67 s () 6.67x 10-6 s () 3.3 x 10-3 s () 13.2 x 10-3 s 1.3. Radio Station KGNU broadcasts at a frequency of 88.5 MHz (88.5 x 10 6 Hz). The wavelength of this signal is about (5 points) (*) 3.4 m () 3.4 km () 34 m () 1.8 m () 1.8 km 1.4. Which of the following statements is true (choose only one answer)? (5 points) (*) The magnification of a pinhole camera increases when the screen used to display the image is moved further away from the pinhole (leaving everything else the same). () The magnification of a pinhole camera increases when the object is moved further away from the pinhole (leaving everything else the same). () The image produced by a pinhole camera is always the same size as the object, but is inverted. () The magnification of a pinhole camera depends on the wavelength of the light that is used to illuminate the object. () The magnification of a pinhole camera depends on the size of the pinhole 1.5. If the index of refraction of a medium is 1.25, the speed of light in that medium is (5 points) (*) 240,000 km/s () 260,000 km/s () 220,000 km/s () 240,000 m/s () none of the above 1.6. The critical angle for total internal reflection at the interface between air and glass is (5 points) () larger for blue light than for red light because the index of refraction for blue light in glass is larger
(*) smaller for blue light than for red light because the index of refraction for blue light in glass is larger () larger for blue light than for red light because the index of refraction for blue light in air is larger () smaller for blue light than for red light because the index of refraction for blue light in air is smaller () the same for blue light and red light 1.7. If a pulse of red light and a pulse of blue light travel in vacuum (5 points) () The red pulse travels faster because its index of refraction is smaller () The blue pulse travels faster because its index of refraction is larger (*) The two pulses travel at the same speed () The relative speed depends on the exact wavelengths of the red and blue pulses () The relative speed depends on the polarization of the two pulses 1.8. If a light wave is traveling in vacuum and its period is doubled then (5 points) () its frequency and its wavelength both double () its frequency and its wavelength are both halved (*) its frequency is halved and its wavelength is doubled () its frequency is doubled and its wavelength is halved () its frequency and its wavelength both increase by the square root of 2 1.9. Two thin magnifying glasses each have the same focal length of 20 cm. What is the effective focal length of the combined lenses when they are touching each other? (5 points) ( ) 5 cm, (*) 10 cm, ( ) 20 cm, ( ) 10 m, ( ) 1 cm 1.10. You are looking towards the sun while standing on Earth in the penumbra of the moon. At that moment you are seeing (5 points) ( ) A total eclipse of the sun (*) A partial eclipse of the sun ( ) A total eclipse of the moon ( ) A partial eclipse of the moon ( ) None of the above Exam Assignment, Part 2 (50 points total) 2.1. Electromagnetic waves propagate with well know velocity of 3 x 10 8 m/s in vacuum (10 points). (a) How far away is the moon if it takes 3 seconds for sunlight reflected from the surface of the moon to reach us (Show your work)? distance = time x velocity. Therefore, distance to the moon = 3s x 3 x 10 8 m/s = 9 x 10 8 m (b) If the index of refraction of glass is 1.5, what is the speed of light in glass? (Show your work)
Speed of light in glass = speed of light in vacuum/refractive index = c/n. So speed in glass = (3 x 10 8 m/s)/1.5= 2 x 10 8 m/s 2.2. Draw the Sun, Moon and Earth during (a) Lunar eclipse and (b) Solar eclipse, and label the various parts of the shadow in both cases (10 points). (a) Lunar eclipse (b) Solar Eclipse Earth Moon Sun 2.3. Explain why an observer sees a fish in water in a location different from its actual position. Show schematically how rays propagate from a fish to the observer s eye. (5 points). The observer sees the fish in a location different from its actual position because of light refraction at the water-air interface.
2.4. White light often splits into colors, as shown in the two examples below (10 points): (a) Explain why white light splits into different colors after passing through a prism and a raindrop. How is this phenomenon called? (5 points for the part (a)). Indices of refraction and velocities of light wave propagation in the prism are different for different colors in the visible spectrum. This results in different angles of refraction of light rays of different color at the air-prism and prism-air (or air-droplet and droplet-air) interfaces. This phenomenon of splitting of white light into light of different colors is called light dispersion. (b) What can you say about the indices of refraction and velocity of waves corresponding to different colors propagating in the medium of a prism/raindrop (glass/water). (5 points for part (b)). In the media such as water and glass, the index of refraction is the largest for the violet light and the smallest for the red light. In these media, red light propagates faster than violet light. In these media, the index of refraction decreases and the speed of light increases with increasing wavelength of light.
2.5. The lens shown below has focal distance f=10m. (10 points) (a). Using two special rays find the image of the red arrow below and then use the 3 rd special ray to verify that your result is correct. (b) Knowing that the distance from the lens to the object (red arrow) is 15m (as marked above), use an appropriate equation and calculate the distance to the image of this arrow. Show your work. 1 1 1 1 1 1 We use the Lens equation = + and find that =. Substituting the distances into f x o x i xi f x o 1 1 1 5 1 the equation, we find = = = and then the distance to the image x i = 30m. x i 10m 15m 150m 30m 2.6. The photo below show a demonstration with rays of light similar to what we had in class previously. There are no mirror surfaces and the materials used in the experimental demonstrations shown below are transparent. Explain the observations and step-by-step describe phenomena that make the light rays changing their propagation direction. (5 points).
This demonstration shows refraction and total internal reflection of incident light rays at the interfaces of transparent media. In the top left photo, the ray is refracted at the air- material interface, then reflected (because of total internal reflection) at the material- air interface and then again refracted at the material- air interface. The same sequence of refraction/reflection/refraction takes place at the bottom left photo. The two right photos demonstrate total internal reflection at one of the material- air interfaces and also straight propagation of the ray incident normally to the air material interface (without changing the direction).