A gaint refrecting telescope at an observatory has an objective lens of focal length `15 m`. If an eye piece lens of focal length `1 cm` is used, find the angular magnification of the telescope.
If this telescope is used to view the moon, what is the diameter of image of moon formed by objective lens ? The diameter of the moon is `3.42 xx 10^6 m` and radius of lunar orbit is `3.8 xx 10^8 m`.

Explanation

Here, `f_0 = 15 cm, f_e = 1.0 cm = 10^-2 m`
(a) Angular magnification `= (-f_0)/(f_e) = (-15)/(106-2) = -1500`
(b) If `d` diameter of the image, then from Fig.
angle subtended by diameter of moon `theta_1 = (l_1)/(r_1) = (3.48 xx 10^6)/(3.8 xx 10^8)`
and, angle subtended by image `theta_2 = (l_2)/(r_2) = (d)/(f_0) = (d)/(15)`
As `theta_2 = theta_1 :. (d)/(15) = (3.48 xx 10^6)/(3.8 xx 10^8)`
`d = (3.48 xx 15 xx 10^-2)/(3.8)`
=`13.73 xx 10^-2 m = 13.73 cm`.
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