REFRACTION LESSON 2
Rules of Refraction for Diverging Lenses
Suppose that several rays of light approach the lens; and suppose that these rays of
light are traveling parallel to the principal axis.
Upon reaching the front face of the lens, each ray of light will
refract towards the normal to the surface.
At this boundary, the light ray is passing from air into a more
dense medium (usually plastic or glass). Since the light ray is
passing from a medium in which it travels relatively fast (less
optically dense) into a medium in which it travels relatively
slow (more optically dense), it will bend towards the normal
line.
Once the light ray refracts across the boundary and enters the lens,
it travels in a straight line until it reaches the back face of the lens.
At this boundary, each ray of light will refract away from the normal to the
surface. Since the light ray is passing from a medium in which it travels
relatively slow (more optically dense) to a medium in which it travels fast (less
optically dense), it will bend away from the normal line.
Because of the different shape of the concave lens, these incident rays are not
converged to a point upon refraction through the lens. Rather, these incident rays
diverge upon refracting through the lens.
What does this mean?
A concave lens can never produce a real image.
Concave lenses produce images which are virtual.
If the refracted rays are extended backwards behind the lens, an important
observation is made. The extension of the refracted rays will intersect at a point.
This point is known as the focal point.
The first generalization can now be made for the refraction of light by a concave lens:
Refraction Rule for a Diverging Lens
Any incident ray traveling parallel to the principal axis of a diverging lens will refract
through the lens and travel in line with the focal point (i.e., in a direction such that its
extension will pass through the focal point).
Now suppose that the rays of light are traveling towards the
focal point on the way to the lens. These rays of light will
refract when they enter the lens and refract when they leave the
lens.
As the light rays enter into the more dense lens material,
they refract towards the normal; and as they exit into the
less dense air, they refract away from the normal. These
specific rays will exit the lens traveling parallel to the
principal axis.
Refraction Rules for a Diverging Lens

Any incident ray traveling parallel to the principal axis of a diverging
lens will refract through the lens and travel in line with the focal point (i.e., in a
direction such that its extension will pass through the focal point).

Any incident ray traveling towards the focal point on the way to the lens
will refract through the lens and travel parallel to the principal axis.
A Third Rule of Refraction for Lenses
Any ray which passes through the precise center of the lens - through the point where
the principal axis and the vertical axis intersect will not have its path changed as it
exits the lens. (Just like for converging or convex lenses)
Step-by-Step Method for Drawing Ray Diagrams
1. Pick a point on the top of the object and draw three incident rays traveling towards
the lens.
Accurately draw one ray so that it travels towards the
focal point on the opposite side of the lens; this ray will
strike the lens before reaching the focal point; stop the ray
at the point of incidence with the lens.
Draw the second ray such that it travels exactly parallel to
the principal axis.
Draw the third ray to the exact center of the lens.
2. Once these incident rays strike the lens, refract them
according to the three rules of refraction for concave
lenses.
The ray that travels towards the focal point will
refract through the lens and travel parallel to the
principal axis.
The ray which traveled parallel to the principal axis on the way to the lens
will refract and travel in a direction such that its extension passes through
the focal point on the object's side of the lens.
The ray which traveled to the exact center of the lens will continue to travel
in the same direction.
3. Locate and mark the image of the top of the object.
The image point of the top of the object is the point where
the three refracted rays intersect. Since the three refracted
rays are diverging, they must be extended behind the lens in
order to intersect.
Draw the extensions until they intersect. All three
extensions should intersect at the same location. The point
of intersection is the image point of the top of the object.
The three refracted rays would appear to diverge from this point. This is
merely the point where all light from the top of the object would appear to
diverge from after refracting through the double concave lens.
4. Repeat the process for the bottom of the object.
If the bottom of the object lies upon the principal axis
(as it does in this example), then the image of this
point will also lie upon the principal axis and be the
same distance from the lens as the image of the top of
the object.
At this point the complete image can be filled in.
NOTICE: In the case of a diverging lens, the image location is located on the object's
side of the lens where the refracted rays would intersect if extended backwards.
The location where the refracted rays are intersecting is the image location. Since
refracted light rays do not actually exist at the image location, the image is said to
be a virtual image. It would only appear to an observer as though light were
coming from this location to the observer's eye.
What charateristics do you notice about the image?
The image is located in front of the lens, it is upright, reduced in size and virtual.
Draw the rays and identify the image for the following objects:
What can you conclude from the image locations of each of the above diagrams?
The diagrams above shows that in each case, the image is

located on the object' side of the lens

a virtual image

an upright image

reduced in size (i.e., smaller than the object)

As an object approaches the lens, its virtual image on the same side of
the lens approaches the lens as well; and at the same time, the image
becomes larger.
Unlike converging lenses, diverging lenses always produce images which share these
characteristics. The location of the object does not affect the characteristics of the
image.
As such, the characteristics of the images formed by diverging lenses are easily
predictable.
EXPERIMENT
In optics, a virtual image is an image in which the outgoing rays from a point on the
object never actually intersect at a point. A simple example is a flat mirror where the
image of oneself is perceived at twice the distance from yourself to the mirror. That is, if
you are half a meter in front of the mirror, your image will appear at a distance of half a
meter inside or behind the mirror.
To contrast, a real image is an image in which the outgoing rays from a point on the
object pass through a single point. It is easiest to observe real images when projected on
an opaque screen. A screen is not necessary for the image to form.[1]

When we look through a diverging lens (at least one concave surface) or look into
a convex mirror, what we see is a virtual image. However, if we observe a
focused image on a screen inside or behind a converging lens (at least one convex
side) or in front of a concave mirror what we see on the screen is a real image
because the image really is at the screen's location. If we position ourselves so
that the screen is directly between ourselves and the optical device (mirror, lens,
etc.), we can remove the screen and still observe the image. It is also important to
note that a converging lens and concave mirror are also capable of producing
virtual images if the object is within the focal length.

For example, a plane or convex mirror forms a virtual image positioned behind
the mirror. Although rays of light seem to come from behind the mirror, light
from the source spreads and exists only in front of the mirror. In drawings of
optical systems, virtual rays are conventionally represented by dotted lines.
Optical rays represent paths on which light actually travels. A virtual ray (the
dotted lines) represent perceived paths as seen by an observer looking into the
optical device. The light rays do not travel on these dotted paths. A point on the
image is located where the virtual rays intersect.
PLAY WITH MIRRORS, FLAT-CONCAVE-CONVEX and LENSES that are
CONVERGING AND DIVERGING.
REFRACTION LESSSON 2 HOMEWORK
1. How can a plane mirror, concave mirror, convex mirror, converging lens and/or
diverging lens be used to produce an image which has the same size as the object?
2. How can a plane mirror, concave mirror, convex mirror, converging lens and/or
diverging lens be used to produce a magnified image?
3. How can a plane mirror, concave mirror, convex mirror, converging lens and/or
diverging lens be used to produce an upright image?
4. How can a a plane mirror, concave mirror, convex mirror, converging lens and/or
diverging lens be used to produce a real image?
5. The image of an object is found to be upright and reduced in size. What type of
mirror and/or lens is used to produce such an image?
6. Draw the rays and identify the image for the following obejcts:
7. The diagram below shows five different object locations. Find their corresponding
image locations.
REFRACTION LESSSON 2 HOMEWORK KEY
1. Plane mirrors will always do this.
Concave mirrors will do this when the object is at C or when the object is right
on the mirror surface.
Converging lenses will do this when the object is at the 2F point or when the
object is right on the lens surface.
Convex mirrors and diverging lenses will only do this when the object is right
on the mirror or lens surface.
2. Plane mirrors, convex mirrors, and diverging lenses will never do this.
Concave mirrors will do this when the object is in front of C.
Converging lenses will only do this when the object is in front of 2F.
3. Plane mirrors, convex mirrors, and diverging lenses will always produce an
upright image.
A concave mirror and a converging lens will only produce an upright image if
the object is located in front of the focal point.
4. Plane mirrors, convex mirrors, and diverging lenses can never produce a real
image.
A concave mirror and a converging lens will only produce a real image if the
object is located beyond the focal point (i.e., more than one focal length away).
5. A plane mirror cannot do this.
A convex mirror and a diverging lens always do this.
A concave mirror and a converging lens can produce an upright image and and
image reduced in size, but never one which is both upright AND reduced in
size.
6. no key
7.