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
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
Remember that convex
lenses are sometimes called "converging
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
upright (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:
- The dashed part of the green line shown above
is a virtual ray.
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.)
- In common with 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
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
The above diagram also illustrates rays diverging
on leaving the second surface of the thin concave
Remember that concave
lenses are sometimes called "diverging
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
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
- 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).
- A ray passing straight through the
centre of the lens.
- 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
The next page is about the lens
muscle of the human
eye (yet to be added).
- Understanding of parts of
the nervous system (such as the eye / visual system)
are required for many exams - e.g. GCSE Physics, GCSE
Biology, and AS and "A"-Level Biology and
Human Biology. Check your syllabus or ask your teacher to find out about the level of detail required.
- Optics and the use of lenses and other optical
components to control the passage of light or
other electro-magnetic energy through systems
is generally studied within the scientific discipline
of physics. Optical system design is a complex
subject, detailed knowledge of which is not necessary
for a basic understanding of how the eye works.
However, because the lens is a very important part of the eye,
and problems with eyesight (vision) are often
treated with the use of spectacles or contact
lenses, this introduction to two very simple types
of lenses is included as background information.