A hobby telescope has an objective lens with a focal length of 58 cm and an eyep

Question

A hobby telescope has an objective lens with a focal length of 58 cm and an eyepiece with a focal length of 8.2 mm. We view the planet Jupiter with this telescope. We do this at the time of year when we are closest to Jupiter, a distance of 6.28 × 1011 m. The diameter of Jupiter is 1.40 × 108 m. (a) Find the diameter (mm) of the image of Jupiter produced by the objective lens. (b) How far (cm) should I place a marble (1-cm diameter) from my eye so that it appears to be the same size as Jupiter as viewed through the eyepiece of the telescope? Give the answers to 2 significant figures.

Explanation / Answer

for a hobby telescope the grossisment is by definition.
G=f2/f1=58/0.82=70.732

the magnification

$M = X2/X1 =Y2/Y14 where

x2=25 cm, x1=6.2810^11 m and Y1=1.410^8 m

M=0.25/6.2810^11 =3.9810^13

hence the diameter of the image is

Y2=Y1M=1.41083.981013=5.57105m=5.57102mm

This must be magnified by the grossisment of the hobby telescope

Y2=GY2=5.5710270.732=3.396 mm

b)
x1/x2=y1/y2

x2=x1y2/y1=0.250.01/0.003396=0.7361m=73.61cm

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