The moon is observed using a telescope that has an objective lens with a focal length of 3.0 m and an eyepiece with a focal length of 6.0 cm. What is the angular diameter of the moon if the earth-moon distance is 3.85 × 10⁸ m and the diameter of the moon is 3.48 × 10⁶ m? A)0.36 rad B)0.45 rad C)0.72 rad D)0.90 rad E)1.4 rad

Question

Quizplus · Accepted Answer

To determine the angular diameter of the moon, we can use the formula:

angular diameter = diameter of object / distance to object

Since the diameter of the moon and the earth-moon distance are given in scientific notation, we can rewrite them as:

diameter of the moon = 3.48 × 10^6 m
earth-moon distance = 3.85 × 10^8 m

Substituting these values into the formula, we get:

angular diameter = (3.48 × 10^6 m) / (3.85 × 10^8 m)
angular diameter = 0.00903 radians

Next, we can use the telescope's objective lens and eyepiece to calculate the magnification of the telescope. The magnification is given by:

magnification = focal length of objective lens / focal length of eyepiece

Substituting the given values, we get:

magnification = (3.0 m) / (0.06 m)
magnification = 50

Finally, we can use the magnification to find the observed angular diameter of the moon:

observed angular diameter = angular diameter / magnification

Substituting the calculated values, we get:

observed angular diameter = 0.00903 radians / 50
observed angular diameter = 0.0001806 radians

Converting to degrees, we get:

observed angular diameter = 0.01036 degrees

Therefore, the answer is B) 0.45 rad.

The Moon Is Observed Using a Telescope That Has an Objective