Question

Any object that just fits into your visual field has this angular size. Do all objects that you see this this angular size have the same linear size (the size you would measure by placing a ruler next to them)? If not, when does an object have a larger linear size than another object even though both have the same angular size?

Answer 1

Answer:

No the angular and linear size will not be same for different objects bearing the same angular size and is dependent on the point of observation. The greater the distance between the observer and the object, the greater the difference between the angular and linear size.

Explanation:

The angular size is the ratio of two lengths namely

$Angular \, Size=\frac{Linear Size}{Distance from the object}$

Here if the distance from the object is unity, the angular and linear size will be similar. However if the distance of observation is very large, the angular size for large bodies with large linear size will be very small.

An example in this regard is Sun.

The linear size of Sun, (the diameter) is 1.3927 million km. Which is very large. However as it is very far from earth, 147.44 million km, the angular size is very small.

it is given as

$Angular \, Size=\frac{1.39}{147.44}=0.009 rad$

Now the same angular size can be of a tennis ball having a diameter of 10 cm , placed at around 10.6 m away.

$Angular \, Size=\frac{0.1}{10.6}=0.009 rad$