Question

A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece of focal length 1.0 cm is used, what is the angular magnification of the telescope?
If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 × 106 m, and the radius of lunar orbit is 3.8 × 108 m.

Answer 1

 

A giant refracting telescope at an observatory has an objective lens of focal length 1.0 cm is used , what is the angular magnification of the telescope ? if this telescope is used to view the moon, what is the diameter of the image of the moon formed by this objective lens? The diameter of the moon is 3.48×106m3.48×106m and radius of the lunar orbit is 3.8×108m3.8×108m

13.73mm13.73cm13.73m1.373cm13.73mm13.73cm13.73m1.373cm

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Solution :

Let d be the diameter of the image angle subtended by the diameter of the moon

θ1=l1r1θ1=l1r1

=3.48×1063.8×108=3.48×1063.8×108

angle subtended by image θ2=l2r2θ2=l2r2

=df0=d15=df0=d15

But θ1=θ2θ1=θ2

∴d15=3.48×1063.8×108∴d15=3.48×1063.8×108

=> d=3.48×15×10−23.8d=3.48×15×10−23.8

=13.73×10−2=13.73×10−2

=13.73cm