The narrow grooves of a CD or DVD act as a reflection Answer Question 30 grating, producing colorful displays.
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Step 1: Understand that the narrow grooves on a CD or DVD are closely spaced and act like a diffraction grating. Show more…
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The diffraction gratings discussed in the text are transmission gratings because light passes through them. There are also gratings in which the light reflects from the grating to form a pattern of fringes. Equation 27.7 also applies to a reflection grating with straight parallel lines when the incident light shines perpendicularly on the grating. The surface of a compact disc (CD) has a multicolored appearance because it acts like a reflection grating and spreads sunlight into its colors. The arms of the spiral track on the $\mathrm{CD}$ are separated by $1.1 \times 10^{-6} \mathrm{~m} .$ Using Equation $27.7,$ estimate the angle that corresponds to the first-order maximum for a wavelength of (a) $660 \mathrm{nm}$ (red) and (b) 410 $\mathrm{nm}$ (violet).
The reflective surface of a CD consists of spirals of equally spaced grooves. If you shine a laser pointer on a CD, each groove reflects circular waves that look exactly like the circular waves transmitted by the slits in a grating. You shine a green laser pointer $(\lambda=532 \mathrm{nm})$ perpendicularly to the surface of a $\mathrm{CD}$ and observe a diffraction pattern on a screen that is $3.0 \mathrm{m}$ away from the CD. You observe that the 1 st order maximum $(m=1)$ appears $1.1 \mathrm{m}$ away from the central maximum $(m=0)$ (a) Determine the distance between the adjacent grooves on a CD. (b) Estimate the total number of bits (units of information) on a CD, assuming that each bit occupies a square with sides that are equal to the distance between the adjacent grooves. Compare the result with the typical data storage of a CD.
The surface of a compact disk (CD) behaves as a kind of diffraction grating. When light is reflected from the surface, each of the closely spaced ridges on a CD behaves as the source of a spherical light wave. Except for the fact that light is reflected rather than transmitted, the effect is the same as for the transmission gratings described in the text; that is, one sees a spectrum of colors (see figure below). Suppose a beam of sunlight is normally incident on a CD. You see yellow light of wavelength 564 nm reflected at an angle of 29.1° relative to the normal. Find the number of ridges per mm on the CD. (Take m = 1.)
Michael S.
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