2.8 Microscopes and telescopes  (Page 6/16)

Summary

• Many optical devices contain more than a single lens or mirror. These are analyzed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray-tracing and thin-lens techniques developed in the previous sections apply to each lens element.
• The overall magnification of a multiple-element system is the product of the linear magnifications of its individual elements times the angular magnification of the eyepiece. For a two-element system with an objective and an eyepiece, this is
  
  $M=m^{\text{obj}}{M}^{\text{eye}}.$
  
  where $m^{\text{obj}}$ is the linear magnification of the objective and $M^{\text{eye}}$ is the angular magnification of the eyepiece.
• The microscope is a multiple-element system that contains more than a single lens or mirror. It allows us to see detail that we could not to see with the unaided eye. Both the eyepiece and objective contribute to the magnification. The magnification of a compound microscope with the image at infinity is
  
  $M_{\text{net}}=\text{−}\frac{(16\text{cm})(25\text{cm})}{f^{\text{obj}}{f}^{\text{eye}}}.$
  
  In this equation, 16 cm is the standardized distance between the image-side focal point of the objective lens and the object-side focal point of the eyepiece, 25 cm is the normal near point distance, $f^{\text{obj}}$ and $f^{\text{eye}}$ are the focal distances for the objective lens and the eyepiece, respectively.
• Simple telescopes can be made with two lenses. They are used for viewing objects at large distances.
• The angular magnification M for a telescope is given by
  
  $M=\text{−}\frac{f^{\text{obj}}}{f^{\text{eye}}},$
  
  where $f^{\text{obj}}$ and $f^{\text{eye}}$ are the focal lengths of the objective lens and the eyepiece, respectively.

Key equations

Conceptual questions