The mirror in an automobile headlight has a parabolic cross-section, with the lightbulb at the focus. On a schematic, the equation of the parabola is given as At what coordinates should you place the lightbulb?
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Two lightbulbs have cylindrical filaments much greater in length than in diameter. The evacuated bulbs are identical except that one operates at a filament temperature of 2100oC and the other operates at 2000oC.
(a) Find the ratio of the power emitted by the hotter lightbulb to that emitted by the cooler lightbulb.
(b) With the bulbs operating at the same respective temperatures, the cooler lightbulb is to be altered by making its filament thicker so that it emits the same power as the hotter one. By what factor should the radius of this filament be increased?
