Understanding Angular Magnification for Objects at Different Distances

In summary: 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).In summary, the textbook said that there is greater linear magnification when the image is focussed at the near point of the eye (25cm) than when the eye is relaxed and the image is at infinity.
  • #1
pivoxa15
2,255
1
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?
 
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  • #2
pivoxa15 said:
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.
 
  • #3
cesiumfrog said:
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.
 
  • #4
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).
 
  • #5
cesiumfrog said:
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?
 

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1. What is magnification?

Magnification is the process of making an object appear larger than its actual size. This is commonly achieved by using a magnifying lens or microscope.

2. How is magnification measured?

Magnification is typically measured in terms of the ratio between the size of the image produced and the size of the original object. For example, a magnification of 2x means the image appears twice as large as the original object.

3. What is the relationship between magnification and distance?

The relationship between magnification and distance is inversely proportional. This means that as the distance between the object and the lens increases, the magnification decreases. Similarly, as the distance decreases, the magnification increases.

4. Can magnification be adjusted?

Yes, magnification can be adjusted by changing the distance between the object and the lens. This is commonly done by either moving the object closer or further away from the lens, or by adjusting the focal length of the lens.

5. What is the maximum magnification possible?

The maximum magnification possible depends on the type of lens or microscope being used. However, in general, the maximum magnification possible is limited by the resolution of the lens or the human eye. Magnifications above 1000x are typically achieved using electron microscopes.

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