Understanding Angular Magnification for Objects at Different Distances

[pivoxa15]

In my textbook when talking about magnification, said "You will notice that there is slightly greater magnification when the image is focussed at the near point of the eye [i.e 25cm] than when the eye is relaxed and the image is at infinity."

I assume they are talking about angular magnification.

How is this true?

The first question is how do you get a magnification if the image is at infinity? Because you can't locate where the image is hence can't measure an angle either?

 

[cesiumfrog]

how do you get a magnification if the image is at infinity? Because you can't locate where the image is hence can't measure an angle either?

Look up at a constellation tonight. The image you see (scorpio or orion say) is effectively an infinite distance from you, and yet you can measure an angle. You can look at the seven sisters, then pull out your binoculars and actually count (uh... is it seven?) them.

 

[pivoxa15]

Look up at a constellation tonight. The image you see (scorpio or orion say) is effectively an infinite distance from you, and yet you can measure an angle. You can look at the seven sisters, then pull out your binoculars and actually count (uh... is it seven?) them.

okay. But the closer the object is to the focus, the greater the linear magnification. This also implies greater angular magnification wouldn't it. So it would be contray to the information in the book.

 

[cesiumfrog]

Linear magnification does not necessarily imply angular magnification (if the image is slightly taller than the original, but much further back, then it will subtend a smaller angle).

 

[pivoxa15]

Linear magnification does not necessarily imply angular magnification (if the image is slightly taller than the original, but much further back, then it will subtend a smaller angle).

Good point. I have created a picture to show what is happening which matches what the textbook say. That is there is greater angular magnification for objects not at the focus.

Ironically, in the textbook they measured the angle from the top ray which is identical for both objects. Is my way of measuring the angle from the bottom ray correct?