How to calculate apparent size of an object based on distance

  • Thread starter dmehling
  • Start date
In summary, the size of the monitor would appear to be 17.6 inches if moved 30 inches away from it, assuming the eye tracking device remains in the same position. This is based on the ratio of 22 inches at 24 inches distance compared to X inches at 30 inches distance. Angular size does not play a role in this problem.
  • #1
dmehling
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I would like to know what the size of my monitor would appear to be if I were to move further away from it. It is a 22 inch monitor, and let's say right now I am 24 inches away from it. If I were 30 inches away from it, what would the size appear to be? I have an eye tracking device mounted on my monitor and it needs to know the size of my screen. If I move the device closer to me but keep the monitor in the same place, I will need to give it different measurements, because it will be as if I have a smaller screen.
 
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  • #2
dmehling said:
If I were 30 inches away from it, what would the size appear to be? I

You have to say precisely what you mean by the size appearing to be something. Are you asking the question:

"A 22 inch monitor at a distance of 30 inches from the eye appears to be the same size as X inch monitor that is 24 inches from the eye. Find X."
 
  • #3
In other words, if I moved further away, it would get smaller. So, it would appear to be a certain size 24 inches away. I would like to know how big it would seem if I moved away another 6 inches, to be a distance of 30 inches away.
 
  • #4
Or maybe I should make it more specific to my situation. I have to tell the software the size of my monitor. If I move the eye tracking sensor further away from the screen, I will have to give new measurements, otherwise the eye tracking will be completely an accurate. So, if I have a 22 inch monitor, and I move the sensor further away from the monitor, it would be like using it on a small monitor.
 
  • #5
No, it will be like using it on the same monitor. The monitor has not changed size.
 
  • #6
No, it would be different. It is the way the sensor is designed. The sensor is tracking my eyes so that I can control the mouse cursor with my eyes. So it needs to know what the size of the monitor is. If the sensor is moved closer to me, but the monitor stays in the same place, the position of my eyes will have changed in relationship to the sensor. Then, the cursor will not be where I'm looking at.
 
  • #7
[itex] \frac{22}{30} = \frac{X}{24} [/itex]

[itex] X = 17.6 [/itex]
 
  • #8
So it's that simple? What about angular size? Does that not play a role in this kind of problem?
 
  • #9
The tangent of the angle that the diagonal of the screen subtends is approximately given by the ratio [itex] \frac{22}{30} [/itex]. Setting the two angular sizes equal implies setting the two ratios equal. You can solve the problem without computing the angles.
 

1. How do I calculate the apparent size of an object based on distance?

The apparent size of an object can be calculated by dividing the actual size of the object by the distance from the observer. This will give you the angular size of the object, which is the size of the object as perceived by the observer.

2. What is the formula for calculating apparent size?

The formula for calculating apparent size is: apparent size = actual size / distance. This formula can be used for any unit of measurement as long as the actual size and distance are in the same unit.

3. Can I use this calculation for objects of any size?

Yes, this calculation can be used for objects of any size as long as the actual size and distance are known. However, for very small objects, the angular size may be too small to accurately measure.

4. Do I need to consider the distance of the object from the observer?

Yes, the distance of the object from the observer is a crucial factor in calculating the apparent size. The farther away an object is, the smaller its apparent size will be.

5. Can this calculation be used for objects that are not at a fixed distance?

No, this calculation is only accurate for objects that are at a fixed distance from the observer. If the distance of the object changes, the apparent size will also change.

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