Waves and Light Test

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1 Name: K T/A C Waves and Light Test Short Answer (Knowledge) 1. Signals from AM stations (frequency range of khz) can often be heard very easily behind large hills, while those from FM stations (frequency range of MHz) cannot. Explain this observation. 2. A new radio station wishes to place two transmission towers near each other in a central location between several urban areas. These two towers will act as a two-point source. If the majority of the population lies on an axis running east west, what orientation should the two towers have in order to maximize the signal reaching the majority of the population? 3. With the aid of a diagram, explain why a bright band occurs on a screen at the central point of Young s double-slit experiment. 4. White light is used to perform Young s double-slit experiment. Describe the pattern that would be observed, and explain why this is observed with specific reference to the central maximum and the remaining bright fringes. 5. What are the two main differences in the pattern observed in Young s double-slit experiment compared to the pattern seen in single-slit diffraction? 6. A student creates single-slit interference as shown in pattern A, below. What physical changes to the experimental apparatus could be made to create interference pattern B? PROBLEMS (T/A) 7. Blue light with a wavelength of 475 nm is passed through a double slit with a separation of 22.6 μm. What is the maximum number of nodal lines visible in the entire pattern? Choose 1 8. A double-slit with a separation of 2.1 μm is used with white light. Find the angular width of the first bright fringe between the violet (λ violet = 400 nm) and red (λ red = 750 nm) end of the spectrum. (Assume two significant digits.) 9. In order to verify that a certain manufacturer produces a double-slit apparatus of the proper slit separation, a laser producing a known wavelength of light can be used for quality control. A helium neon laser produces a monochromatic light source with a wavelength of nm. The manufacturer claims that the slit width is 205 μm ± 3%. The apparatus produces an interference pattern with the laser such that the distance between the first and seventh nodal lines is 56.9 mm on a screen 3.00 m away. Is the apparatus being produced within the acceptable limits? 10. A single-slit with a width of 23.2 μm is used to create a pattern on a screen 1.5 m away. Find the angular separation between the two third-order bright fringes (away from the central maximum) in the pattern if a 575 nm light source is used. Choose The thickness of a human hair is to be measured using the interference pattern produced by an air wedge. Red light with a wavelength of 638 nm is used on an air wedge that is 25.0 cm long. If 10 bright fringes are counted across 1.06 cm in the air wedge, what is the thickness of the hair? 12. Currently, CD players use a laser diode producing light with a wavelength of 780 nm. The index of refraction of the polycarbonate plastic layer is If blue laser light with a wavelength of 475 nm were to be used, by what amount would the depth of the pits in the CD surface need to be changed? 1

2 SHORT ANSWER 1. ANS: Since both types of signals are radio waves, they travel at the speed of light. AM signals have a much lower frequency than FM signals and, therefore, have a much longer wavelength. (Wavelength is inversely proportional to frequency.) Longer wavelengths exhibit diffraction much more easily, which allows the AM signals to bend around the large hill and reach the receiver, while the FM signals cannot bend to reach the receiver. REF: MC OBJ: 9.2 LOC: WA ANS: The wavelength must be more than or equal to the size of the opening for diffraction to be observable. REF: K/U OBJ: 9.2 LOC: WA ANS: - The towers should be arranged so that they lie on an axis which runs north south. - This will create an interference pattern with a central maximum located perpendicular to the axis joining the two towers. - The central maximum will run east west, reaching a majority of the population with the maximum signal strength. REF: MC OBJ: 9.3 LOC: WA ANS: The central point is located equidistant from each of the two slits. Since the light through each slit originates from a single source, it is coherent (in phase) when it leaves the slits and reaches the centre of the screen in phase. This creates constructive interference, or in the case of light, a bright band. REF: C OBJ: 9.5 LOC: WA ANS: - The central maximum would remain white since all colours interfere constructively at this point. - The remaining bright fringes would show the spectral colours, since each colour has a different wavelength. - Each would interfere constructively at different distances from the central maximum. - Red would appear on the outside of each bright fringe, farther from the central maximum, since it has the longest wavelength and would diffract the most. - Violet would appear on the inside, closer to the central maximum, with the remaining spectral colours arranged in order. REF: C OBJ: 9.6 LOC: WA3.03 2

3 6. ANS: - Light that travels through the atmosphere is polarized by the small particles within the atmosphere. - The direction of polarization depends on the location of the Sun and the direction being viewed. - Certain animals have eyes that are sensitive to polarized light and can thus determine the direction they are travelling based on this observation. REF: MC OBJ: 10.1 LOC: WA ANS: - In Young s experiment, all the maxima are equal width, while in single-slit diffraction, the central maximum is twice as wide as the rest. - In single-slit diffraction, the intensity of each maximum decreases as you move away from the central maximum, while in double-slit diffraction, the intensities remain fairly constant. REF: I OBJ: 10.2 LOC: WA ANS: Since, three variables could be changed - the distance to the screen L could be increased - the wavelength of the light could be increased - the slit width w could be decreased REF: I OBJ: 10.2 LOC: WA2.02 PROBLEM 9. ANS: The maximum number of nodal lines in the pattern is 96 (48 on each side of the central maximum). REF: K/U, C OBJ: 9.5 LOC: WA ANS: 3

4 The angular width of the first bright fringe is 9.9 o. REF: K/U OBJ: 9.5 LOC: WA ANS: 4

5 Since the actual slit separation is within the stated range ( μm), the apparatus is acceptable. REF: MC OBJ: 9.5 LOC: WA ANS: The angular separation between the two maxima is 9.95 o. REF: I, C OBJ: 10.2 LOC: WA ANS: 5

6 The thickness of the hair is 75.2 μm. REF: I OBJ: 10.4 LOC: WA ANS: The CD reading head uses the properties of interference such that the pit depths are of the light in the polycarbonate plastic layer. 6

7 The pit depth would change by 49 nm. REF: MC OBJ: 10.5 LOC: WA3.02 7

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