# Object visibility and size-to-distance ratios

1. Aug 8, 2011

### jimgavagan

Kind of just a random question I thought of that I thought was a physics question - I apologize in advance if it is not a physics question.

Here goes:

What is the relationship between the size of an object and the distance from your eye at which the object becomes non-visible? Obviously the larger an object, the longer the distance at which the object remains perceptible, but I'm sure the size-to-distance ratios for all objects are the same, no?

2. Aug 8, 2011

### xts

Depends how bright the object is. You may see something really small (e.g. laser pointer aimed at you) from several miles.

3. Aug 8, 2011

### Drakkith

Staff Emeritus
Well, there are 2 different things here. The first is the resolution of your eye and the apparent size of what you can see. The other is the luminosity of the object. For example, your eye is not able to see the "size" of a star in the sky. But the amount of light it emits causes it to be visible even as a "point object".

4. Aug 9, 2011

### mikeph

Yes, you can use similar triangles to show that an object that is twice as far but twice as large will appear the same shape in the human brain. Other posters made the important point that if the object is radiating isotropically, the intensity of light falls like 1/r^2. So this object, when expanded and moved twice as far away, will have the same shape but not the same brightness.

5. Aug 9, 2011

### jimgavagan

I understand the brightness thing, but let's just assume there's not a lot of light anywhere in this scenario. I'm just wondering if the ratio of the distance-to-size of an object is the same for all objects regardless of initial size at 0 distance and, if it is the same for all objects, what that ratio approximately is.

Assume that all objects do not radiate light and do not reflect light.

I'd also note though that clearly a silver balloon let go into the sky reflects light and yet there's a certain distance at which it's no longer perceptible.

6. Aug 9, 2011

### xts

Absolute darkness. Under such scenario you would see nothing, I am afraid.

7. Aug 9, 2011

### jimgavagan

Note I did not say absolute darkness, but dimness.

8. Aug 9, 2011

### Drakkith

Staff Emeritus
I believe you want the inverse-square law or something similar. For example, if I double the distance from an object, both its X and Y length appear to decrease by half. The means that the apparent area of the object is now 1/4 what it was.

See here: http://en.wikipedia.org/wiki/Inverse-square_law

9. Aug 9, 2011

### jimgavagan

Inverse square law looks right. So how do we solve the inverse square equation to figure out the distance at which an object becomes imperceptible given the size of the object?

10. Aug 9, 2011

### Drakkith

Staff Emeritus
Imperceptible meaning that you can't see the object's SIZE? Or imperceptible that we can't see it because it becomes so dim?
The star Deneb has a radius of 1 AU, meaning that its physical size is the same as the radius of Earths orbit around the sun, yet we cannot see its size. However Deneb has such luminosity that we can still see it from Earth. This is because the angular resolution of our eye is not enough to see the apparent size, but it can see the intensity of the light as a point source.

11. Aug 9, 2011

### DaveC426913

No. This cancels out.

When you expand it, you are expanding it squared. Square A, whose surface is 10mx10m (100m^2) at 100m distance will have the same apparent brightness as Square B, whose surface is 20mx20m (400m^2) at 200m distance.

This is obvious if you note that, since square A will exactly and perfectly eclipse square B, their light cones are also identical.

This is also obvious if you close one eye. Without contextual clues, you will not be able to tell if you are looking at Square A, 100m away, or Square B, 200m away. (That's partly why we have two eyes.)

Last edited: Aug 9, 2011
12. Aug 9, 2011

### DaveC426913

The one thing that will not scale is imperfectly-transparent air.

On earth, a 1m object at 100m will be noticeably higher in contrast than a 100m object at 10,000m.

13. Aug 11, 2011

### jimgavagan

Drakkith: Yes, I mean imperceptible in size - nothing to do with brightness/dimness.

DaveC:

"On earth, a 1m object at 100m will be noticeably higher in contrast than a 100m object at 10,000m."

This is more along the lines of what I'm getting at. So, why wouldn't they be the exact same apparent size, then? What distance would the 100m object have to be to appear to be the same size as the 1m object at 100m?

14. Aug 11, 2011

### DaveC426913

They would be exactly the same apparent size. :grumpy:

10,000m!

You didn't read what I wrote. The contrast will be higher (more blacks and whites = more visible), but this is due to atmospheric effects.

If you eliminated atmo effects (say, doing the experiment in space) (and also eliminating parallax clues), a 1m object at 100m would be totally indistinguishable from a 100m object at 10000m.

15. Aug 11, 2011

### DaveC426913

What?

Last edited by a moderator: May 5, 2017
16. Aug 11, 2011

### maruthisarat

when the distance of any object is less than 25cm,It become invisible (or) less quality.this is the nature of human eye.
In humans there exists two types of sights.those are
1.short sight
2.long sight

1:-short sight means the persons have some distinct area around himself.That area only be seen by him.
2:-long sight means the person have some distinct area around himself.That area could not be seen by him.He can see the surroundings out of this area.

17. Aug 11, 2011

### DaveC426913

No. It may be out of focus, but he will most certainly be able to see it.

There is a continuum, which includes both 1] and 2] as well as neither 1] nor 2].

Again, no. It may be out of focus, but he will most certainly be able to see it, whether he is near-sighted or far-sighted.

18. Aug 11, 2011

### maruthisarat

No,when the distance is less than 25cm,he can see but it is not clear.
To prove put your palm 25 cm before eye and move it towards your eye.
Then eye is strained and image will be not clear.

Last edited: Aug 11, 2011
19. Aug 12, 2011

### DaveC426913

Correct.

The first time you said this you were claiming it would be "invisible". Perhaps just a poor choice of word?

20. Aug 12, 2011

### Drakkith

Staff Emeritus
Exactly, the image will be out of FOCUS and will appear blurry. Invisible means that something is completely incapable of being seen in any way.