The laser in a compact disc player must precisely follow the spiral track on CD, along which the distance between one loop of the spiral and next is only about 1.25 micrometre. The figure shows how a diffraction grating is used to provide information to keep the beam on track. The laser light passes through a diffraction grating before it reaches the CD. 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 designed to fall on the flat surfaces on both sides of the information track and are used for steering. As long as both beams are reflecting from smooth, nonpitted surfaces they are detected with the constant high intensity. If the main beam wanders off the track, however one of the side beams begins to strike pits on the information track and the reflected light diminishes. This change is used with an electronic circuit to guide the beam back to the desired location. Assume the laser light has a wavelength of 780 nanometers and the diffraction grating is positioned 6.90 micrometres from time disk. Assume the first-order beams are to fall on the CD 0.400 micrometre on either side of the information track. What should be the number of grooves per millimetre in the grating?
