Polarized light is incident on 7 polarizing sheets. the axis of the first polarized sheet makes an angle θ with the plane of polarization. each subsequent sheet has an axis that is rotated by an angle θ from that of adjacent sheets. find θ if 92% of the incident intensity is transmitted by the sheets. ° suppose you want to rotate the plane of polarization of a beam of polarized light by 65°, but you do not want the final intensity to be < 66% of the initial intensity. what is the minimum number of polarizing sheets you must use? sheets

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time ∆t. the resistance of the coil is r, and the total charge is q = i∆t, where i is the average current induced by the change in flux. (b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly “swiped” past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip. (c) is it necessary that the credit card be “swiped” through the reader at exactly the right speed? why or why not?