| MadSci Network: Physics |
Greetings:
I wish a teacher had answered your questions for me when I was in the 5th grade. Teaching science in grades K-6 is especially challenging but it is very important because many of us decided to be scientists between grades 5-9.
Your question is a bit complex because it has 2 optical systems in it, the magnifying lens and the human eye, also there are variable distances. I'll start by making a simple comment about the eye then after discussing the magnifying lens the students will also understand more about how the eye works . Also, we will fix the distance between the object being viewed and the lens and only move the viewing eye (Scientists always try to reduce the number of variables in an experiment).. We will use only one eye for viewing, closing the other to eliminate binocular vision effects.
Trying to explain your question with out a simple demonstration would probably not be understood by the students (at any grade level). Once the simple experiment is set up nothing need be changed for the students to view (and hopefully understand) the phenomena you question.
HUMAN VISUAL PERCEPTION (simplified)
An simple object (in this case a candle and flame) emits and reflects light
in many directions (thousands of angles as in Figure 1). If the very small
aperture of the eye (about one millimeter) is close to the candle
(position 1) it gathers rays between rays A & E and the object fills the
retina and appears large (close). At position 2 the eye gathers rays
between B & D and the flame appears smaller. At position 3 the eye gathers
rays only around ray C and the flame appears smaller yet. At 100 yards the
eye would gather only a single ray and the flame would be a point of light
in the distance. When I was in the army we observed that the dark adapted
eye could see a candle flame several miles away!.
A B
/ *
/ *
/ *
/ *
/ * I
()-1-2----3------ C <--EYE APERTURE
I I\ * I (NOT TO SCALE)
I I \ *
I I \ *
I I \ *
____ \ D
CANDLE E
FIGURE 1
From our lives experience we conclude that the number of rays (angles)
that we can observe from an object (with one eye) helps us to determines
how far away an object is. Baby's grasp for things they can not reach
until they learn how to perceive distance. Also; we must remember that
optical illusions can fool all of us at times in our visual perception.
CONVEX OPTICAL LENS
When a light ray passes from air into glass or when it travels out of
glass into air the ray bends at the air/glass surfaces. This bending is
called REFRACTION and the amount of bending is determined by the angle
that the glass surface makes relative to the light ray. (Refraction is
caused by the glass slowing the speed of light which can be graphically
demonstrated. Perhaps this is a topic for another question to the Mad
Scientist). Only if the glass surfaces are parallel will a light ray pass
through the glass with out bending (e.g. a window pane). The surfaces of a
convex lens are precisely curved so that each light ray entering the lens
parallel to the lens axis is refracted differently causing all rays to
converge to a FOCAL POINT (FP) as shown in Figure 2.
LENS
/\ /
--> -------------------I I /
I I\ /
PARALLEL LIGHT I I \ /
RAYS COMING I I \ /
I I \ /
AXIS 2FL-------FP-----I----I-------FP-------2FL------3FL AXIS
I I / \
FROM THE SUN, I / \
MOON OR A I I / \
DISTANT LIGHT I I/ \
--> -------------------I I \
\/ \
<--FOCAL-->
FIGURE 2 LENGTH
FOCAL LENGTHS
First we must measure the focal length of the magnifying
lens. The following experiments would be best observed if the
magnifying lens is at least 4 inches in diameter, otherwise
a darkened room will be required to observe the phenomena.
The lens' focal length can be determined by focusing a
distant light source such as the sun or the moon on a
thin white paper. The distance from the lens to
the focal point is the FOCAL LENGTH (FL) of the lens. Turn
the lens around so that the light comes through the lens in
the other direction and check the FL again. Most common
magnifying lenses have equal (symmetrical) FLs on either
side of the lens. An important point to make to the class
is to NEVER LOOK AT THE SUN THROUGH ANY TYPE OF OPTICS. The
danger of this to the eyes can be demonstrated by burning a
hole in a piece of paper using the suns rays.
REAL IMAGES
Now set up the experiment in Figure 3. Make a ruler on a
large paper labeling the FL distances on each side of the lens and also
mark 2 times the FL and 3 times the FL on each side of the lens.
CANDLE (OBJECT) LENS
/\
()------------------I I
I I\ * I I\ I
I I \ * I I \ I<--THIN PAPER
I I \ * I I \ I (IMAGE PLANE)
I I \ * I I \ I
I I \ * I I \ I
2FL------FP--------I-*--I--------FP--------2FL---------3FL-
\ I I * \ I I
\ I I * \ I I
\ I I * \ I I <--REAL IMAGE
\I I * \I I
I I------------------*()------
\/ \ *
\ *
\
FIGURE 3
Candles make a simple bright object; however, if there are safety concerns,
a small white frosted Christmas tree light bulb can also be used. Place the
candle 2 FLs on the left side of the lens and move a thin sheet of white
paper to a point 2 FL on the right side of the lens where the candle flame
is sharply imaged on the paper. This is called the REAL IMAGE and the paper
defines the IMAGE PLANE. The paper should be thin enough so that you can
see the image from the right side of the experiment through the paper.
Optical physics also teaches us that a real image at the 2FL point will
be of the same size as the object (unity magnification)
except the REAL IMAGE IS INVERTED from the object.
Now repeat the experiment with the candle at 1 1/2 FL (half way between FL and 2FL). Now the REAL IMAGE should be at 3FL on the right and it should be twice the size of the object only inverted (magnification = 2X).
ANSWERING THE QUESTION
A simple answer to your question would be to look at Figure 3 and note
that at 2 FL the converging rays from all points on the candle (not just
one point on the flame as illustrated) cross over each other exchanging
the top rays from the object with the bottom rays and vice versa.This
crossover inverts all virtual images viewed at distances greater than 2FL.
To observe and to answer the other parts of your question reset up the experiment in Figure 3 with the object distance at 2FL. Observe and note the location of the real image at 2 FL on the paper. Now remove the paper and look at the object through the lens with your eye at about FP. The object appears right side up. This is called a VIRTUAL IMAGE because it cannot be projected on a paper, it is formed in your eye. Now move your eye slowly back toward 2FL and the VIRTUAL IMAGE of the candle enlarges. Why? Because as you move back you are now gathering more rays (angles) not less. This is the opposite of what happens in Figure 1 because the lens makes the rays converge not diverge as they would in nature. When you reach 2FL the virtual image becomes jumbled right at the point of the real image where the rays in Figure 3 cross over each other. You cannot see the real image at 2FL because it is on the surface or inside your eye around 2FL (to close for your eye to focus on). Remember the real image is inverted. Why? Look at the ray diagram in Figure 3. The three rays from the flame tip pass through lens , are diffracted and cross over each other at the real image (2FL). The top rays become the bottom rays and the bottom rays become the top rays. At greater viewing distances a new virtual image is formed at the point of the inverted real image. If you ploted rays from all points on the candle, not just from the tip of the flame as shown in Figure 3, they all would cross over at 2FL. .As you move back to 3FL the rays are diverging just as the do in Figure 1 and the images gets smaller with distance. It is also interesting to move your eye sideways during the experiments and note which way the images move relative to the way the eye is moved. This also switches at 2FL because of the crossover.
Unlike our experiment, during normal use a magnifying lens is moved while the object and eye distances are fixed. This moves the focal plane (real image) back and forth and produces the same result as our experiment except that the magnification of the real image also changes as the object to lens distance changes, confusing and complicating the problem.
As an aside, the human eye is a convex lens with a focal length of about one inch. The world is viewed as an inverted real image projected on the retina (in place of the paper). However; our brain adapts to the inverted image and we move about seeing the world upside down!
Cameras place film in the focal plane and slide and movie projectors use a screen in the focal plane to view the progected and magnified real images. All of these images are inverted so we have to pplace the slides and movie film (objects) upside down in the projectors so that the real images are right side up for viewing.
I know this explanation has been a bit complicated. I would like to have your comments on how the experiment worked and what points your students have problems with. Perhaps we can work them out. My company is starting a K-12 project and we will be interacting with studens at your grade level.
Regards
Adrian Popa your Mad Scientist