Image 1 Caption: A diagram illustrating the behavior of lenses and curved mirrors in the limit of Gaussian optics which assumes paraxial approximation: i.e., assumes that light rays make small enough angles to the optical axis that the small angle approximation for the trigonometric functions is valid. Image formation is described below and illustrated in Image 2.

Features:

1. Going down the diagram the optical devices are as follows: converging (biconvex) lens, diverging (biconcave) lens, concave mirror, convex mirror.

2. The dashed line is the optical axis which is the symmetry axis of an optical device.

3. F is the focal point (AKA principal focus).

4. The two red lines for each case represent a continuum set of light rays parallel to the optical axis impacting on the optical device and then (converging to)/(diverging from) the focal point.

5. The focal point is defined by the (converging to)/(diverging from) behavior it causes the continuum set of light rays to do.

6. f is focal length. It is the distance from a fiducial point on the optical axis (illustrated in the diagram for each case) to the focal point.

7. In the limit of Gaussian optics, parallel light rays offset by an angle θ from the optical axis will (converge to)/(diverge from) a point on the focal plane (a plane perpendicular to the optical axis passing through the focal point) in a cone whose symmetry axis is offset from the optical axis by angle θ likewise.

8. In the limit of Gaussian optics, simple formulae can be given for image formation: 1) for curved mirrors, the Gaussian mirror equation, 2) for lens, the thin lens formula.

9. The light rays from a point source of light that are parallel to 1st order in small angle offsets are at optical infinity by definition. Such light rays are treated as exactly parallel in the limit of Gaussian optics.

10. An extended object at optical infinity will create an image on the focal plane which can be viewed on a screen or transformed in some other way (e.g., with an eyepiece of a telescope).

11. The extended object can be treated as a continuum of point sources of light with each point source of light offset from the others in angle as viewed from the optical device.

    

12. Image 2 Caption: A diagram of a Keplerian (refractor) telescope. It is a refractor telescope because it uses a lens (which works by refraction) as primary (i.e., the light-gatherer) rather than a curved mirror which works by reflection).

13. The image formation in the focal plane is illustrated. The image is a real image in that light rays are actually there. A in a virtual image, the light rays merely trace back to the apparent image location and are NEVER actually there.

14. The light gathering power of a telescope scales as the diameter squared of the primary.

15. The eyepiece allows the observer to view the real image with some specified magnification. Note, the greater the magnification of the eyepiece, the smaller the field of view (FOV): there is a trade-off.

16. The image has a point inversion (i.e., 180° rotation about the optical axis). This is why Keplerian telescopes have always been primarily used for astronomy. It does NOT matter if the image point inverted in visual astronomy---real visual astronomers want point inversion---and NOT at all in astronomical imaging (AKA astrophotography).

17. The Keplerian telescope was invented as design and published Johannes Kepler (1571--1630) Dioptrice (1611) (Wikipedia: Refracting telescope: Keplerian telescope), but it seems Kepler NEVER built one himself:
    Google AI question: Did Kepler ever build a Keplerian telescope?: "No, Johannes Kepler (1571--1630) never built a Keplerian telescope. While he described the theoretical optical design using convex lenses in his Dioptrice (1611), he was a theoretician and mathematician rather than a scientific instrument maker. The first known Keplerian telescope constructed was sometime in the time span 1613--1617 by Jesuit Christoph Scheiner (1573--1650)." (Somewhat edited.)

    The Keplerian telescope has a much wider field of view (FOV) and greater eye relief than the Galilean telescope which was improved and used by Galileo (1564--1642) from 1609, but it was invented in 1608 in the Netherlands, but it NOT certain by whom (Wikipedia: History of the telescope).

    The point inversion made the Keplerian telescope less attractive for non-astronomical purposes. Sailors didn't care for it---how to you know if a flag is the Jolly Roger is if it point inverted?

1. Credit/Permission: © User:Henrik, 2008 / CC BY-SA 3.0.
   Image link: Wikimedia Commons.
   Local file: local link: optics_lens_curved_mirror.html.
   
2. Credit/Permission: © Szocs Tamas (AKA User:Tamasflex, 2009 / CC BY-SA 3.0.
   Image link: Wikimedia Commons: File:Kepschem.png.