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in Optics by (63.5k points)

(a) 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?

(b) 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.

1 Answer

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Best answer

f0 = 15m, fe = 1.0 cm = 10–2m.

(a) Angular magnification = f0/fe = 15/10-2 = 15 x 102 = 1500

(b) Angle subtended by the diameter of the moon = Arc/radius = (3.48 x 106)/(3.8 x 108)

Angle subtended by image

= Arc (diameter of image)/radius (focal length of objective) = d/f0 = d/15

∴ d/15 = (3.48 x 106)/(3.8 x 108)

⇒ d = (3.48 x 15)/(3.8 x 102) = 13.73 x 10-2m = 13.73 cm.

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