Angular magnification what is angle subtended?

In summary, when using a simple microscope, the angular magnification is calculated by dividing the angle subtended at the eye by the angle without the instrument. However, there may be confusion about which angle to use, as shown in the example image. This is because the angle measured farther out may appear larger, but in reality, the angle measure remains the same regardless of where it is measured.
  • #1
gracy
2,486
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In case of simple microscope .we take angular magnification
I know The angular magnification of an instrument is the ratio of the angle subtended at the eye when using the instrument divided by the angular size without the instrument
But what I am not getting is how this subtended angle is taken?
For example in the image below
angel subtended.png

Is it because this angle theta is negligible (nearly zero)
 
Last edited:
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  • #2
In your picture you ask "why can't we take the angle [itex]\theta[/itex] as the angle subtended rather than [itex]\alpha[/itex]?". But I see NO difference between "[itex]\theta[/itex]" and "[itex]\alpha[itex]". You also say "Is it because this angle theta is negligible (nearly 0)".

Are you possibly thinking that the angle, measured farther out, is larger than the angle measured close to the vertex? If so, then you do not what "angle measure" means!
 
  • #3
HallsofIvy said:
Are you possibly thinking that the angle, measured farther out, is larger than the angle measured close to the vertex?
Yes.
 
  • #4
HallsofIvy said:
"angle measure" means!
Hmm... I got you point.This picture greatly explains that there is n difference between difference between "θ" and ",alpha
 

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1. What is angular magnification?

Angular magnification is a measure of how much larger an object appears when viewed through a lens or optical instrument, compared to how it would appear to the naked eye. It is expressed as the ratio of the angle subtended by the image to the angle subtended by the object.

2. How is angular magnification calculated?

Angular magnification is calculated by dividing the angular size of the image (measured in radians) by the angular size of the object (also measured in radians). This ratio is then expressed as a decimal or percentage.

3. What is the angle subtended?

The angle subtended is the angle formed between two lines drawn from the observer's eye to the ends of an object or image. In the context of angular magnification, it refers to the angle formed between the observer's eye, the object, and the center of the lens or optical instrument.

4. How does angular magnification affect the appearance of objects?

Angular magnification makes objects appear larger or smaller depending on the ratio between the angle subtended by the image and the angle subtended by the object. A larger angle subtended by the image will result in a larger angular magnification and a larger apparent size of the object.

5. What factors affect angular magnification?

The main factors that affect angular magnification are the focal length of the lens or optical instrument and the distance between the object and the observer's eye. A longer focal length will result in a larger angular magnification, while a shorter distance between the object and the observer's eye will also increase the angular magnification.

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