Question

an astronomical telescope has an objective of focal and 200 cm and eye piece of focal length 10cm. an observer adjust the distance of the eyepiece from the objective to obtain the image of the sun on the screen 40cm behind the eye piece. the diameter of the sun's image is 6.0 cm. find the diameter of the sun. the average earth to sun distance is 1.5 * 10^11 m.

Answer 1

diameter of the sun is 1.5 × 10^9 m

given, focal length of eye- piece , fe = 10cm

focal length of objective, fo = 200cm

so, image of sun on the screen, ve = 40cm

using formula, 1/ve - 1/ue = 1/fe

⇒1/40 - 1/10 = 1/ue

⇒-3/40 = 1/ue

⇒ue = -40/3

so, magnification produced by eye piece, me = |ve/ue| = 40/(40/3) = 3

hence, the size of image formed by objective = size of object/me = 6/3 = 2

if D is the diameter of sun, angle subtended by it on its objective, α = D/(1.5 × 10¹¹)

further, angle subtended by the image, α = size of image/focal length of objectives = 2/200 = 1/100

so, α = 1/100 = D/1.5 × 10¹¹

D = 1.5 × 10^9 m

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Answer 2

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An astronomical telescope has an objective of focal and 200 cm and eye piece of focal length 10cm. an observer adjust the distance of the eyepiece from the objective to obtain the image of the sun on the screen 40cm behind the eye piece. the diameter of the sun's image is 6.0 cm.