Question

An astronomical telescope is used in normal adjustment when looking at the moon. If the objective has f1=60cm and that of the eye piece is f2=1cm. Suppose the moon has a diameter of 4.50*10^6m and the distance of the moon from the earth is 4.84*10^8m, find the angle of the image of the moon that is subtended by the astronomers eyes.

Answer 1

Answer on Question #69262, Physics / Optics

An astronomical telescope is used in normal adjustment when looking at the moon. If the objective has f1=60cm and that of the eye piece is f2=1cm. Suppose the moon has a diameter of 4.50*10^6m and the distance of the moon from the earth is 4.84*10^8m, find the angle of the image of the moon that is subtended by the astronomers eyes.

Find: β - ?

Given:

f1=60cm

f2=1cm

D=4.50×10⁶ m

a=4.84×10⁸ m

Solution:

Angular diameter of the Moon:

$$\delta = 2 \arctan \left(\frac {D}{2 d}\right) = 2 \arctan \left(\frac {4 . 5 \times 1 0 ^ {6}}{2 \times 4 . 8 4 \times 1 0 ^ {8}}\right) = 0 {}^ {\circ} 3 2 ^ {\prime} (1),$$

where D is the diameter of the observed object, a is the distance of the observed object from the observer

Of (1) ⇒ α=0.533°

Magnification of the telescope:

$$k = \frac {f _ {1}}{f _ {2}} = \frac {\beta}{\alpha} (2),$$

where $f_1$ is the focal length of objective, $f_2$ is the focal length of eye piece, $\alpha$ is the angular diameter of the observed object, $\beta$ is the angular diameter of the observed object in the telescope

Of (2) ⇒ β = f₁/f₂ α (3)

Of (3) ⇒ β=31.98°

Answer:

31.98°

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