Question
Suppose one of the 10-m-diameter Keck Telescopes in Hawaiicould be trained on San Francisco, 3400 km away. Wouldit be possible to read a) newspaper headlines or b) a billboardsign at this distance? Justify your answers by giving theminimum separation resolvable with Keck at 3400 km, assuming 550-nmlight. c) Repeat for the case of the Keck optical interferometer,formed from the two 10-m Keck Telescopes and several smaller ones,with an effective aperature of 50 m. Suppose one of the 10-m-diameter Keck Telescopes in Hawaiicould be trained on San Francisco, 3400 km away. Wouldit be possible to read a) newspaper headlines or b) a billboardsign at this distance? Justify your answers by giving theminimum separation resolvable with Keck at 3400 km, assuming 550-nmlight. c) Repeat for the case of the Keck optical interferometer,formed from the two 10-m Keck Telescopes and several smaller ones,with an effective aperature of 50 m.
Explanation / Answer
The resolution of a telescope is given by min = 1.22 * (/D) = 550 nm = 550 * 10^-9 m D = 3400 km = 3400 * 10^3 m or min= 1.22 * (550 * 10^-9/3400 * 10^3)= 1.6 * 10^-11 rad Any two objects that subtand an angle greater than or equal tothis value are resolved.Therefore,we can read a newspaper headlinesor a billboard sign at this distance. c)the condition for maxima in the interference pattern at theangle bright is d * sinbright= m * m =0,±1,±2,............... d = (1/50) m = 0.02 m = 20 * 10^-3 m = 20 mm and m = 1 sin1 = ((1) * /d) = (550 * 10^-9/20 * 10^-3) =0.0000275 or 1 = sin-1(0.0000275) =0.0015o