We
can use the rules in the previous topic (Topic
23. Thin Lenses, part 2. Ray tracing rules) to construct the image produced
by a positive lens in a number of different situations.
1.
The object is beyond the first focal point, but is at a finite distance from
the lens:
Using
the three rays defined in the previous topic, we can see that the image is
real, inverted and beyond the second focal point on the image side of the lens.
The
image is real because the rays on the image side of the lens from any point on
the object really do converge to a single point on the image. If we look into
the lens from the image side, we see the rays appearing to diverge from the
image that is formed.
The
magnification (the ratio of the size of the image to the size of the object)
depends on the exact position of the object. The magnification is less than 1
(that is, the image is smaller than the object) when the object is very far
away, and it slowly increases as the object approaches the lens. It is exactly
1 when the object is twice the focal distance away from the lens, and continues
to increase as the distance is reduced still further. The lens produces a
magnified image when the object is located at a distance of less than twice the
focal length (but greater than the focal length) from the lens.
Note
that in addition to getting larger, the image moves away from the lens (to the
right) as the object approaches the lens.
2.
The object is at the first focal point on the left side of the lens.
Since
every ray leaving the object passes through the focal point, all of the rays
emerge parallel to the axis on the right-hand side of the lens. A point object
located at this position therefore produces a parallel beam of light.
Note
that this configuration can be used to show that a beam of parallel light
striking the lens is imaged to a point of light at the focal point. This
configuration is simply the inverse of the situation that is shown and would be
realized by simply interchanging the object and the image.
This
configuration can be used to determine the focal length of a positive lens – it
is simply the location of the image when the object is very far away. As a
practical matter, an object distance of more than 10 times the focal length is
sufficient for most purposes.
3.
The object is inside of the first focal point on the left side of the lens.
The
blue ray that leaves the object comes off at the same angle as a ray that
originated at the focal point, which is to the left of the object in this
situation. Therefore, this blue ray is bent so that it emerges parallel to the
axis on the right side of the lens.
The
green ray that leaves the object heading towards the center of the lens passes
through the lens without any change in direction.
The
rays do not converge to an image on the right hand side of the lens, but rather
appear to be coming from a larger image that is behind the object. Note
that the rays only appear to be coming from this image, so that this image is
virtual rather than real. It is also erect – that is it has the same
orientation as the object and it is magnified – its size is larger than the
size of the object.