GEOMETRIC OPTICS
FOCUSED ENLIGHTENMENT
“RAYS-ED” IMAGES
The first investigation concerns the angle between light rays from an object
which reach a detector. Below is a sketch of an eye and the silhouette of
the disk. Light rays from the edges of the disk to the eye are shown.
What happens to the angle between the rays as the disk moves away from
the eye?
Suppose the disk were a mile away, what would the angle between the rays
be like? If the disk were a thousand miles away? On the Sun (93 million
miles away)?
If the rays were approximately parallel, how far away would the disk be?
Place the multi-slit mask in the ray box and adjust
the slide on the box to make the rays parallel.
This is most simply done by shining the rays along
the lines on the graphs. We will use this
configuration for the next few experiments.
LENS
Place the ray box on the left and the biconvex lens on the silhouette on the
graph. With the parallel rays from the left passing through the lens, sketch
where the light rays go. Measure the distance from the center of the lens
to the point where the light rays converge (+ if to the right of the lens, - to
the left).
length = ______________ cm.
LENS
As before, place the lens on the silhouette with the light coming from the
left. Draw in lines where the light rays go. If the actual rays don’t cross at
a point, extend them back with dotted lines to find a crossing point. As
before, measure the length from the lens center to the crossing point. Use
a negative sign if the intersection is for the dotted lines.
length = _____________ cm.
REFLECTIONS ON MIRRORS
With the light from the left, place the curved mirror on the curves,
reflective side to the left, and sketch the light rays, as before. Measure
the distance from the center of the mirror to the intersection point,
recording a – sign if the intersection is behind the mirror.
length = _____________ cm.
length = _____________ cm.
RELATING THE MEASUREMENTS TO NEWTON’S LENS EQUATION
(Homework)
In the previous lab, Newton’s lens equation was introduced to relate the
object distance, image distance and something called the focal length of a
lens.
1/f = 1/o + 1/i
For the four investigations above, you have measured the image distance:
the distance from the lens or mirror to the image.
From the first activity, what happens to the angle between the incoming
rays as the object (point of divergence) moves farther away from the lens
(disk)?
If the parallel rays from the light box are coming from an object, how far
away must it be? (Recall the discussion on page 1)
Using this object distance and your measured image distances, find the focal
lengths for each optical element.
Biconvex lens :
f = _______ cm.
Biconcave lens :
f = _______ cm.
Concave mirror :
f = _______ cm.
Convex mirror :
f = _______ cm.
LAW OF REFLECTION:
Replace the mask on the ray box so that the single narrow slit is down, giving
a single ray.
On the following polar graph paper, place the flat mirror with its face along
the dark line and bring the single ray in along a radial line. Draw in the
reflected ray. Repeat this three more times, bringing the light ray in along
different lines each time.
How do the angles of the incoming and reflected ray compare? Make sure
your statement of the relationship works for all your observations.
Jello optics
Curvature and focal length of lenses
To investigate the effect of the curvature of the surface on the focal
length of the lens, you will get to make your own lenses and use the same
procedure as for the lenses above.
Each group will have a small pan of jello, empty cans of different radii, a
plastic knife to remove the jello from the pan and a light box.
You will make three optical elements from the jello:
 two biconvex lenses of different curvature
 a long, straight “light pipe”
The two lenses are cut from the jello with the two different cans by
overlapping the cuts they make:
A. With the two lenses and the light box, find out what effect the
difference in curvature has on the focal length.
B. Optical fibers and total internal reflection.
Take your jello light pipe and place it on a flat surface with a slight S-curve
in it. Be careful not to cause any breaks or small nicks in the jello.
Shine the laser pointer in one end and note where the light comes out of the
jello. You should be able to see the path of the light inside as the laser is
visible. Draw a diagram of the light beam passing through the jello.
What happens if there is a nick on the side and the laser beam hits it?
Ray diagrams and predictions about images.
Light from an object like a light bulb is given off in all directions. When we
use a lens or mirror, not all the light waves are of interest.
Only those which are incident on the optical element are of any importance.
Of these, we can use three to figure out where the image is, what the
magnification is and whether it is real or virtual.
Two diagrams for a biconvex (convergent) lens:
.
Image is real,
inverted and
magnified
Image is virtual, erect and
magnified.
A real image can be projected on a screen, a virtual image cannot. A virtual
image is not formed by light rays actually converging; it is a point where light
rays from the lens appear to come from when viewed by eye or instrument.
Your image in a plane mirror appears to be behind the mirror inside the wall,
which is not physically possible; this is a virtual image.
For any ray diagram, there are three useful rays which can be used to find
the image:
From the top of the object through the center of the lens and straight on.
From the top of the object horizontal to the lens, then through F2
From the top of the object through F1 to the lens and horizontal.
If the lens is biconcave (divergent), then the locations of F1 and F2 are
reversed, as below:
virtual
erect/inverted
magnified by _____
real/virtual
erect/inverted
magnified by _____
A combination of lenses. Two converging lenses are used to produce a
magnified image. Note the second lens uses the virtual image from the first
lens as its object.