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1.A beam of 541-nm light is incident on a diffraction grating that has 400 grooves/mm.
(a) Determine the angle of the second-order ray.
(b) What If? If the entire apparatus is immersed in water, what is the new second-order angle of diffraction?
(c) Show that the two diffracted rays of parts (a) and (b) are related through the law of refraction.
2.The laser in a CD player must precisely follow the spiral track, along which the distance between one loop of the spiral and the next is only about 1.25 /m. A feedback mechanism lets the player know if the laser drifts off the track, so that the player can steer it back again. Figure P38.30 shows how a diffraction grating is used to provide information to keep the beam on track. The laser light passes through a diffraction grating just before it reaches the disk. The strong central maximum of the diffraction pattern is used to read the information in the track of pits. The two first-order side maxima are used for steering. The grating is designed so that the first-order maxima fall on the flat surfaces on both sides of the information track. Both side beams are reflected into their own detectors. As long as both beams are reflecting from smooth non-pitted surfaces, they are detected with constant high intensity. If the main beam wanders off the track, however, one of the side beams will begin to strike pits on the information track and the reflected light will diminish. This change is used with an electronic circuit to guide the beam back to the desired location. Assume that the laser light has a wavelength of 780 nm and that the diffraction grating is positioned 6.90 /m from the disk. Assume that the first-order beams are to fall on the disk 0.400 /m on either side of the information track. What should be the number of grooves per millimeter in the grating?
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3.An optical pin is placed midway between two parallel plane mirrors M1 and M2 which are 10 cm apart. How far from the pin is the fourth reflected image?
4.An optical pin is placed midway between two parallel plane mirrors M1 and M2 which are 10 cm apart. How far from the pin is
the fourth reflected image?
5.Two plane mirrors are placed parallel to each other and 40 cm apart. An object is placed 10 cm from one mirror. Determine the
(b) Second smallest
(c) Third smallest (occurs twice), and
(d) Fourth smallest distance of the object?
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