A hobby telescope has an objective lens with afocal length of 70 cm and an eyepi

Question

A hobby telescope has an objective lens with afocal

length of 70 cm and an eyepiece with a focal length of 8.2 mm. Weview the

planet Jupiter with this telescope. We do this at the time of yearwhen we are closest to

Jupiter, a distance of 6.28 × 10 raised to the11th m. The diameter of Jupiter is 1.40 × 10 raisedto the 9th m. (a) Find

the diameter (mm) of the image of Jupiter produced by the objectivelens. (b) How far

(cm) should I place a marble (1-cm diameter) from my eye so that itappears to be the

same size as Jupiter as viewed through the eyepiece of thetelescope? Give the answers to

2 signi?cant ?gures.

Explanation / Answer

I used yournumbers, but you do not have the correct diameter of Jupiter. Itshould be only 1.40 x 108 meters, not109. Let me know if you made a mistake. Send me aprivate message. (a)    diameter of image / diameter ofJupiter = focal length / distance to Jupiter .          diameter ofimage / 1.40 x 109   = 0.70 / 6.28 x 1011 .          diameter ofimage =   0.001561 meter =    1.561 mm =    1.6 mm . (b)    the angular magnification is  f1/f2 = 70 / 0.82 =    85.37 .     The angular diameter of Jupiteris         diam of Jupiter/ distance to Jupiter .     Angular diameter of imageis      ang mag * diam of Jupiter /distance to Jupiter .     Angular diameter of marbleis     diameter of marble / distance tomarble . The latter two are equal, so... .      diam of marble / distance tomarble = ang mag * diam of Jupiter / distance toJupiter .        0.01 / distto marble = 85.37 * 1.40 x 109 / 6.82 x1011 .          0.01 / distto marble   =    0.1752 .         dist tomarble   =    0.057 m =   5.7 cm .          0.01 / distto marble   =    0.1752 .         dist tomarble   =    0.057 m =   5.7 cm

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