Question

What is the angular size of the Moon if viewed from a binocular that has a focal length of 1.2 cm for the eyepiece and a focal length of 8 cm for the objective? Use the radius of the moon 1.74×10⁶ m and the distance of the moon from the observer to be 3.8×10⁸ m.

a. 3.86×10⁻³ radians
b. 4.25×10⁻³ radians
c. 5.12×10⁻³ radians
d. 2.94×10⁻³ radians

Answer 1

The angular size of the Moon when viewed through the specified binoculars is approximately 4.25×10⁻³ radians.

Step-by-step explanation:

The question asks about the angular size of the Moon when viewed through binoculars with given focal lengths for the eyepiece and the objective. The angular size, θ, can be found using the formula θ = 2 * arctan(⅒ / D), where r is the radius of the Moon and D is the distance from the Moon to the observer. Substituting the given values, we have θ = 2 * arctan(1.74×10⁶ / 3.8×10⁸). Calculating this value, we get θ ≈ 4.25×10⁻³ radians, which is option b.