Aparant size of an object based on distance from it.

  • Thread starter Runaway
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In summary, we can use the concept of creating a "cone" with two skinny triangles to determine the apparent size of an object at a certain distance. In this case, we can find the apparent size of the Earth from half way between the Earth and the moon by using trigonometry to solve for the angle of the cone. The long side of the triangle represents the distance between the observer and the object, while the short side is one-half the size of the object.
  • #1
Runaway
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Is there an equation I could use to determine how big something would appear to be at a certain distance from said object?

In particular I want to find how big the Earth would appear to be from half way from the Earth to the moon if a picture was taken of it with 1x zoom. in other words, how big would a sphere with a diameter of 12,756.1 km appear from 192,201.5 km away?
 
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  • #2
Hey Runaway,

It's actually pretty simple. Just draw a long skinny right triangle. The long side of the triangle is the distance between the observer and the object. The short side of the triangle is one-half the size of the object. If you put two of these skinny triangles side by side, you'd make a "cone." The angle at the tip of the cone is the apparent size of the object.

Are you comfortable with the trigonometry involved in solving for the angle?

- Warren
 

1. What is the definition of apparent size?

The apparent size of an object is the size it appears to have from a certain distance, as perceived by the human eye. It may differ from the actual size of the object due to factors such as distance, perspective, and visual illusions.

2. How is the apparent size of an object affected by its distance from the observer?

The apparent size of an object decreases as its distance from the observer increases. This is because the further away an object is, the smaller it appears to the human eye. This is known as the distance-size illusion.

3. Can the apparent size of an object change even if its actual size remains the same?

Yes, the apparent size of an object can change based on the distance from the observer. For example, a person standing 10 feet away from you will appear smaller than the same person standing 5 feet away, even though their actual size has not changed.

4. How does the angle of view affect the apparent size of an object?

The angle of view, or the angle between the observer's line of sight and the edges of the object, can affect the apparent size of an object. A larger angle of view can make an object appear larger, while a smaller angle of view can make it appear smaller.

5. Can the apparent size of an object be manipulated?

Yes, the apparent size of an object can be manipulated through various optical illusions and techniques. For example, using forced perspective, where objects are placed at specific distances and angles to create the illusion of different sizes, can change the apparent size of an object.

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