What is angular size and how does distance affect it and the object's apparent brightness?

What is angular size and how does distance affect it and the object's apparent brightness?

• A. Angular size is the angle an object subtends; it increases with distance.
• B. Angular size is the angle an object subtends; it decreases with distance.
• C. Angular size is the distance to an object; brightness does not depend on distance.
• D. Angular size is how large an object appears from a given distance; closer objects have larger angular sizes, and brightness falls roughly as 1/r^2.

Answer: (D)

Angular size is the angle an object subtends at your eye or at a detector. For a fixed physical size, that angle gets smaller as distance increases, approximately θ ≈ size/distance in radians. So moving farther away makes the object look smaller, and halving the distance makes it look about twice as large. Brightness, or apparent brightness, follows the inverse-square law: the light from the object spreads over a sphere whose surface area grows with distance squared, so the observed brightness falls as 1/distance^2. In other words, objects look dimmer the farther away they are, and the drop is proportional to the square of the distance. Putting those ideas together, the statement that angular size describes how large something appears from a given distance, that closer objects have larger angular sizes, and that brightness falls roughly as 1/r^2 is the accurate description. The other ideas—angular size increasing with distance, or angular size equaling distance, or brightness not depending on distance—don’t match how angles and light behave in space.

Angular size is the angle an object subtends at your eye or at a detector. For a fixed physical size, that angle gets smaller as distance increases, approximately θ ≈ size/distance in radians. So moving farther away makes the object look smaller, and halving the distance makes it look about twice as large.

Brightness, or apparent brightness, follows the inverse-square law: the light from the object spreads over a sphere whose surface area grows with distance squared, so the observed brightness falls as 1/distance^2. In other words, objects look dimmer the farther away they are, and the drop is proportional to the square of the distance.

Putting those ideas together, the statement that angular size describes how large something appears from a given distance, that closer objects have larger angular sizes, and that brightness falls roughly as 1/r^2 is the accurate description. The other ideas—angular size increasing with distance, or angular size equaling distance, or brightness not depending on distance—don’t match how angles and light behave in space.