Weber's law of just noticeable difference

[SoggyBottoms]

Homework Statement

This question is about the line length experiment, which can be seen here: http://people.usd.edu/~schieber/coglab/WebersLaw.html

Basically you are shown two lines and you have to pick the one that is longer. This is repeated X number of times and the results allow you to calculate the smallest detectable difference in line length, the threshold.

1) If the lines are now made twice as long and the viewing distance stays the same, what will happen to the threshold?

2) If the viewing distance is doubled, but the lines stay the same length, what will happen to the threshold?

The Attempt at a Solution

1) I expect that the threshold is a fixed percentage of line length, so if the line length doubles, so would the threshold.

2) I expect it would double again, but I'm not sure how to back that up.

 

[Ignea_unda]

Homework Statement

This question is about the line length experiment, which can be seen here: http://people.usd.edu/~schieber/coglab/WebersLaw.html

Basically you are shown two lines and you have to pick the one that is longer. This is repeated X number of times and the results allow you to calculate the smallest detectable difference in line length, the threshold.

1) If the lines are now made twice as long and the viewing distance stays the same, what will happen to the threshold?

2) If the viewing distance is doubled, but the lines stay the same length, what will happen to the threshold?

The Attempt at a Solution

1) I expect that the threshold is a fixed percentage of line length, so if the line length doubles, so would the threshold.

2) I expect it would double again, but I'm not sure how to back that up.

This is the first time I've ever heard of this experiment, but when you speak of "viewing distance" do you mean the the distance between you and the object? Think about what that would do to your perceived length. How does the appearance of an object change if you double the distance between you and the object?

 

[SoggyBottoms]

This is the first time I've ever heard of this experiment, but when you speak of "viewing distance" do you mean the the distance between you and the object?

Correct.

How does the appearance of an object change if you double the distance between you and the object?

I suppose the perceived length either drops off linearly or quadratically?

 

[Ignea_unda]

I suppose the perceived length either drops off linearly or quadratically?

Alright. Then if the threshold is a fixed percentage of length (or more accurately, perceived length), what would the threshold do?

 

[SoggyBottoms]

If linearly, then it would double. If quadratically, then it would quadruple. Just going by my gut feeling I would say perceived length drops off quadratically with distance. Is that correct?

 

[Ignea_unda]

If linearly, then it would double. If quadratically, then it would quadruple. Just going by my gut feeling I would say perceived length drops off quadratically with distance. Is that correct?

Honestly, I don't know. I wish I could be of more help, but I've never read anything dealing with perceived size.