Magnification formula for a Galilean telescope

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SUMMARY

The discussion focuses on deriving the magnification formula for a Galilean telescope, specifically the relationship between the outgoing rays and the optical axis in terms of the focal lengths f1 and f2, and the incident angle α. The general magnification formula is established as -f1/f2, while the effect of the angle α on the outgoing rays is explored. It is clarified that parallel rays entering the telescope remain parallel upon exit, and the angular magnification is defined as the ratio of the angle subtended by the object at the eye through the telescope to the angle subtended without the telescope.

PREREQUISITES
  • Understanding of optical principles, specifically ray diagrams.
  • Familiarity with the concepts of focal lengths in lenses, particularly f1 and f2.
  • Knowledge of angular magnification and its calculation.
  • Basic skills in geometry related to angles and triangles.
NEXT STEPS
  • Research the derivation of the Galilean telescope magnification formula.
  • Study the principles of ray optics, focusing on parallel rays and their behavior through lenses.
  • Explore the concept of angular magnification in more depth, including practical applications.
  • Investigate the differences between Galilean and other types of telescopes, such as Keplerian telescopes.
USEFUL FOR

Students studying optics, physics educators, and anyone interested in understanding the mechanics of telescopes and magnification principles.

Cocoleia
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Homework Statement


I am asked to draw the ray diagram
for an incident plane wave whose rays are at an angle α with respect to the optical axis of the telescope. I have done this, but I need to find an expression for the angle between the outgoing rays and the optical axis, in terms of f1, f2, and α . f1 is the focal length for the converging lens and f2 is the focal length for the diverging lens

Homework Equations

The Attempt at a Solution


I know that generally the magnification would be (-) f1/f2. I am wondering how the angle α will affect this. As to the actual question at hand, I am unsure how to proceed. I believe that the rays are not outgoing at an angle of α, but otherwise I am unsure.
 
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Cocoleia said:
the angle between the outgoing rays and the optical axis, in terms of f1, f2, and α
As I understand it, parallel rays entering the telescope emerge still parallel. If opposite edges of some distant object subtend an angle θ at the telescope, and the telescope has magnification m, what angle must the rays from one edge and rays from the other edge form on exit from the telescope?
 
The magnification that you mention Cocoleia is the angular magnification.
It is the ratio of the angle subtended by the object at the eye when the object is viewed with telescope, or the angle of the image formed by the telescope, divided by the angle of the object when viewed without the telescope.
 

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