. A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of ua = 36.2°, the ray refracted into the water makes an angle of 49.8o with the normal to the interface. What is the smallest value of the incident angle ua for which none of the ray refracts into the water?

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?

Most short-period comets do not have randomly oriented orbits because

The energy released by a nuclear fusion reaction is produced when