# Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position. A giant refracting telescope at an observatory has an objective lens of focal length 15 m and an eyepiece of focal length 1.0 cm. If this telescope is used to view the Moon, find the diameter of the image of the Moon formed by the objective lens. The diameter of the Moon is $3.48 \times 10^{6} m$, and the radius of lunar orbit is $3.8 \times 10^{8} m$.

Answers (1)

Magnification

$m=\frac{f_o}{f_e}=\frac{15}{0.01}=1500$

focal length of the objective  $f = 15m$

let  $d_1$  be the diameter of the image of the moon which is formed by the objective lens.

Now,

the angle subtended by diameter of the moon = the angle subtended by the image,

$\frac{d}{r}=\frac{d_1}{f}$

$\frac{3.48*10^6}{3.8*10^8}=\frac{d_1}{15}$

$d_1=13.74 cm$

The diameter of the image of the moon is 13.7 cm.

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