Concave and Convex Lenses ()

This follows the page introducing simple lenses, focal length and focal point.

The ray diagrams below represent light passing through simple convex and concave lenses.

Although the following notes don't include discussion of refractive indices, the re-direction of the light passing through these lenses is due to the effect of refraction, i.e. when the light enters and leaves the lenses at the air-glass and glass-air interfaces.


Ray Diagram of light passing through a thin Convex Lens

As shown above, a thin convex lens forms a real (meaning that rays of light actually pass through it!) but inverted (upside-down) image of a real object located beyond the focus of the lens.

The above diagram also illustrates rays converging on leaving the second surface of the thin convex lens.

Remember that convex lenses are sometimes called "converging lenses".

The lens in the human eye is a convex lens.

An equivalent diagram of light leaving an object then passing through a concave lens is included below for comparison.

Ray Diagram of light passing through a thin Concave Lens

As shown above, a thin concave lens forms a virtual (meaning that rays of light do not actually pass through it!) but
(that is, the same way up as the object; not upside-down) image of a real object located beyond the focus of the lens.

Virtual Rays and Virtual Images:

  1. The dashed part of the green line shown above is a virtual ray.
    Virtual rays are theoretical constructs that can be useful for explaining/understanding certain situations - but they are not paths along which light really travels. (It is possible to arrange experiments to demonstrate this.)
  2. In common with virtual rays, virtual images are also theoretical constructs that can be useful for explaining/understanding certain situations. However, they are not real - meaning that actual rays of light do not pass through the points defining a "virtual image", hence it is not possible to see a virtual image (in the same way as one can see a real image by placing a screen at the location of the "image" - onto which a real image would be formed).
    Recall, for comparison, that in the case of image formation in the eye, a real image is formed on the retina - the retina being the screen on which the real image is formed.

    A useful way to think of virtual images is as locations from which light appears to have come.
    (School Physics textbooks usually include several examples of ray diagrams involving virtual images.)

The above diagram also illustrates rays diverging on leaving the second surface of the thin concave lens.
Remember that concave lenses are sometimes called "diverging lenses".

This concludes the introduction to, and comparison of, simple thin convex and thin concave lenses.
Scroll up to review the differences between the two ray diagrams on this page.

The following further explanations include more detail - beyond the scope of some introductory courses about the eye.

Ray Diagrams - Reminders and Further Explanations

Ray Diagrams are used to show how electro-magnetic radiation (such as rays of light) move through an optical system such as a camera, telescope, binoculars, or the human eye, e.g. ray diagram of image formation within the eye.

Notes Re. Drawing Ray Diagrams:

In the cases of image-forming systems, at least 2 rays must be traced through the "optical system" (e.g. the eye) from each point on the object in order to show (i.e. for purposes of illustration rather than calculation) in the ray diagram the corresponding position of that point on the image. The corresponding position in the image space is the point at which rays coming from that point on the object meet again, i.e. where those rays cross each other.

However, in many cases the purpose of drawing a ray diagram is to find out about the existence (or not) and, if present, about the location, size, orientation, and quality of an image - rather than just to illustrate what is already known.

When a ray diagram is drawn to find out how rays pass through a simple thin lens 3 key rays are usually drawn.
This set of 3 rays is a standard way of simplifying the passage of light through thin lenses so that it can be more easily remembered, drawn, and understood. It is, of course. a simplification because using the Law of Refraction would require knowledge of refractive indices and angles of incidence (not just the focal length of the lens), and calculations of angles of refraction for each ray at each surface.

The 3 key rays shown in the diagrams above and can be listed as follows:

  1. A ray propagating parallel to the optical axis, to the centre of the lens, then through F (though in the case of concave lenses, the "ray" through F will be virtual).
  2. A ray passing straight through the centre of the lens.
  3. A ray through F to the lens, then parallel to the axis.

Note that simple "teaching" examples may be designed so that the rays from a point on the object all pass through exactly the same point in the image space whereas in real systems rays in the image space may not pass precisely through a single point, but rather an area - whose size has implications for the "sharpness" of the image, and hence the quality of the image and the particular optical system that formed that image.

The next page is about the lens and ciliary muscle of the human eye (yet to be added).