(Central Pest Control) SHADOWS

The experiments went well and we were able to try a few of these experiments with our students. Some things I would like to point out involve the flagpole experiment. We constructed a graph to plot the shadow height and true height of several objects. We continued the trajectory of the height line to estimate how tall the flagpole is. This worked well but you have to be careful with the x and y axis to keep them the same intervals.

As we worked through the activities it appeared we were getting deep into a singular activity with different links but when we went to the table of contents we had actually moved on to different checks from the table of contents.

Discussion Questions:

2.Margie is correct. The shapes on the bulb would not create an image on the inside of the lampshade. The hearts and spades would project too large of a shadow being on the bulb. The 100 watts letters are on top of the bulb and the ceiling is too far away to produce the image.

Joe's comments:

This depends a lot on whether Louise is using frosted or unfrosted bulbs. With frosted bulbs the light is leaving the surface of the bulb in all directions, and the part she has decorated will perhaps change the color of the light hitting that side of the shade a little bit, but not give any image. If she uses unfrosted bulbs, light travels in straight lines from the filament, and a really big drawing on the bulb would give a somewhat fuzzy image on the lampshade -- it depends on whether the drawing is bigger than the filament, or not, and whether the bulb surface is closer to the filament or to the shade (well, it's closer to the filament. So things are not going to work very well).

3.The top of the flagpole only blocks a certain portion of sunlight. The base of the flagpole produces the sharp part of the shadow. The fuzzy top part of the shadow is caused by the sunlight that is not blocked. I have an image drawn in my notebook that helps describe this. The tree is also a tall object and only blocks certain portions of sunlight. The faint ones are like the fuzzy parts the shadow and are created by the top leaves. The dark area under the shade tree is completely in the shadow from sunlight. The bright discs are from the narrow gaps between the branches and leaves that provide no shade.

Joe's comments:

OK. I think the point is that the sun is not a point on the sky -- it is a disk. Then light coming from the right and left hand side of the sun are travelling slightly different directions, and the resulting shadows are in different places. The fuzziness gets worse, the farther it is from the object making the shadow to where the shadow is seen.

With the tree, a tiny gap in the leaves lets sunlight through, and the beam spreads out for the same reason just described. The spot on the ground is a disk because the sun is a disk. During a partial eclipse of the sun, the spots are all crescent shaped.

Here is a picture of the situation --

Pictures from http://www.pa.uky.edu/~straley/virtual/light/sshad.htm

(Cordia Lions)

1. If you wanted to study something very tiny, like a pinhead, could you use the technique of Shadows #2 activity to produce a large shadow of it? Why or why not?

Answer: Yes you could produce a large shadow of it. The closer to the light source, the larger the shadow of the object regardless of the size of the object. However, it may be so large that it becomes very fuzzy so there is a limit to the distance allowed for a distinct shadow.

2. Louise has a great idea how to decorate her living room for when she hosts the bridge club next week: she will draw hearts and spades on the light bulbs, so that they project these pictures onto the lampshade and the ceiling. Easy to do, cheap, and after the party she can just wash the pattern off. Margie objects, "If that works, why doesn't it say '100 Watts' on the ceiling already?" Is Margie right, that this won't work? Or can you tell Louise how to rescue the scheme?

Answer: In order for Louise to be a cheap skate, she could draw hearts and spades on the light bulbs, but we think she would need extra lenses to focus the light more in order to show the shadow of the objects.

Joe's comments:

I should mention that the discussion questions do not in general have Right Answers that I know and you are supposed to provide. Rather, they provide a context to talk about the content of the unit.

I like the answer to #1 more, because you explain the principle (how shadow size is determined) and consider a possible complication (fuzziness). We need to worry about fuzziness more: if you try this experiment (definitely allowed), you will find that the shadow of the pinhead doesn't seem to get bigger at all as you move it away from the light -- it just fuzzes out. The point is that the filament of the clear light bulb is bigger than the pin head, and so it is like trying to make a shadow of your finger with a frosted bulb. Light coming from the different parts of the filament can reach almost all points behind the pin, and that makes for a fuzzy shadow. To magnify the pin head this way, we need a very tiny light source.

Your answer to #2 is a possible solution, and after you have done the lenses section we can discuss how to make it work (I'm going to add your proposal to the discussion page for lenses -- thanks for the idea!). But the question for today is whether it will work at all, just writing on the light bulb. So please try to answer this one again. Here's two big hints: Margie and Louise are both right (No Right Answers), and the first question you should ask yourself is what kind of light bulbs is Louise using?

(Guest commentator)

> 1. When  you study something small like the head of a pin  it will not help
> you to see the object any better by casting a shadow of it. To get a sharp
> shadow you will need to keep the pin further away from the light source
> which will result in a small shadow, not much bigger than the actual size of
> the pin head. When you attempt to enlarge the shadow by moving the object
> closer to the light source the result is a fuzzy shadow and of course it
> would be better to use a clear light bulb.
>

Joe's comments:

I should mention that the discussion questions do not in general have Right Answers that I know and you are supposed to provide. Rather, they provide a context to talk about the content of the unit.

I like this answer, because you explain the principle (how shadow size is determined) and consider a possible complication (fuzziness). We need to worry about fuzziness more: as you note, you will find that the shadow of the pinhead doesn't seem to get bigger at all as you move it away from the light -- it just fuzzes out. The point is that the filament of the clear light bulb is bigger than the pin head, and so it is like trying to make a shadow of your finger with a frosted bulb. Light coming from the different parts of the filament can reach almost all points behind the pin, and that makes for a fuzzy shadow. To magnify the pin head this way, we need a very tiny light source.

>
> 2. This seemed to be the easiest to me.
> I would suggest that in order to project hearts and spades onto the wall
> that they cut out shapes of hearts and spades, attach the shapes to stands
> and place the objects in front of a light source with a clear bulb and they
> should see the hearts and spades on the wall.
>

Joe's comments:

That will work. But what about Louise's idea? Her idea has the advantage that she can write with colored ink and get red hearts and black spades. Or are you siding with Margie? Then you should explain to Louise what goes wrong.

>
> 3. This seemed to be the hardest for me.
> The sun is so large that when it's rays strike a tall object  some rays come
> from the top of the sun and other rays come from the bottom areas of the
> sun. This produces a "fuzzy" region in tall objects that may not be there in
> shorter objects. The width of the fuzzy zone gets wider as you move further
> from the object making the shadow. The spots of sunlight seems harder for me
> to figure out. I think that it has something to do with where the leaves are
> on the tree. Maybe the sharply focused leaves are at the bottom of the tree
> and the overlapping fuzzy leaves are closer to the top of the tree.

Joe's comments:

The flagpole question is discussed on one of the pages in the unit ( http://www.pa.uky.edu/~straley/virtual/sunsh.htm on the internet -- perhaps D:/sunsh.htm will work without having to go on the internet). Leaves at the bottom of the tree give sharper shadows, but I tried to find scenes where there weren't any of these. I see round disks in the picture -- don't you? Now you have to think about the second picture shown at http://www.pa.uky.edu~straley/virtual/sshad.htm and imagine that instead of the top of a flagpole we had a small hole between leaves. The beam that this defines spreads out as shown, giving a disk. A bug sitting anywhere in the disk would see the sun through the hole in the leaves; a bug sitting elsewhere would just see the sky. It is an image of the sun (and during eclipses, the shape changes from disks to crescents!).

(Dark Brigade)

Question #1: The question we are the most sure about.
Yes, you can use the technique of adjusting the distance of the object between the light source and the screen as we found in Shadows #2. However, we were not able to maintain a larger sharp image in this activity. We found that the closer the object was to the light source, the fuzzier the image became on the screen. When the object was placed closer to the screen the image was sharper but was not as large. (We used both a frosted and clear bulb of different sizes with no significant difference in the results.)

Joe's comments: So at the end of the day, we can't magnify a pinhead to any good effect? But it works fine for a bowling ball, so what is the relevant condition? Where does the fuzzitude come from? Can you imagine or design a light source that would be useful in magnifying a pin head, or at least a pencil eraser?

Question #2: The question we are the least sure about.
We feel that there are too many variables in this question, such as the type of material for the shade, materials for the markings, and the position of the lamp itself. Based on this we feel that it will not work. In our experiment we found that the translucent material of our "lamp shade" allowed us to see the design fairly well approximately 20cm from the bulb, but did not project on the wall. Instead, we would suggest using a floodlight to project the image of a heart or spade on the ceiling or wall...similar to the Christmas images that will project onto houses. This way the old ladies will still be able to see their cards. ;-)

Joe's comments:

I'm glad to see that you tried this. This is always the right answer, and very much the point of view that we are trying to foster.

There certainly are many variables, and that's why Louise needs your advice. We can't let know-it-all Margie get away with this -- let's put a heart on the ceiling, even if it is rather fuzzy.

The spotlight suggestion is a bit unsatisfactory -- how does the spotlight get around the problem?

Actually, this question and the pinhead question are the same one (when Louise has the sewing circle over, there will be pinheads on the ceiling? I don't think so).

My apologies for turning your answers back into questions -- but the ideas underlying these questions are major foundations of what we will be doing later, and it's important to understand them.

(Newtons)

Shadows Question 1 Yes, make sure it is between the light source and the shadow. Also, using the transparent light bulb will make the object more focused. The bigger the object you use, the larger the shadow created. Another point is the way the object is hit by the light.

Joe's comments:

The question asked how to make the shadow of a pinhead large and sharp. Using a clear light bulb is certainly one thing we need to do, but how do we control how large it is, and make it as unfuzzy as possible? Did you try to do it (definitely allowed)?

Question 2 The height difference at the top and bottom makes a difference. The rays coming from the top edge of the sun make a shadow at a slightly different place than the rays from the bottom edge of the sun. The angle is different.

They are brighter because the sun's light is hitting that spot more than one direction at a time. Tha also explains the overlapping.

Joe's comments:

My question was, why are they disks at all? Why not leaf-shapes? Here is a detail of one of the pictures -- I see round disks. Why?

see http://www.pa.uky.edu/~sciworks/images/dapple3.jpg

(Perfectionists)

We decided to send the answer to question one as the question that we were the most confident that was correct. We decided that it was possible to use the same method as activity number two used to produce a nice sharp shadow. In order to do this, we would have to use a small, non-frosted light source. We prefer an incandescent light because there are no color variations with the spectrum. The light source would have to be at a stationary point that would direct the light to a point. Next, the pinhead would have to be placed close to the light souce in a direct path of the light rays. The pinhead would have to be at least four times the distance, if not more, between the light source and the pinhead from the wall where the shadow would be projected. A shadow will be larger if the object is closer to the light source than the wall where the shadow would appear.

Joe's comment:

DId you try it (definitely allowed!)?

You have the main points of the theory correct. The trick to this question is realizing that fuzziness is going to be a real problem, and so the light source will have to be small, and of course not frosted. But when we say small, we have to mean, the filament is smaller than a pinhead! Or else light will surely get around the pinhead to any point on the screen.

We can't buy that kind of light bulb at KMart, but you can make one, by punching a very small hole in a piece of aluminum foil and taping it to a light bulb. Now the hole becomes the light source for the pinhead. It wouldn't be very bright, but it would work.

This basically is what happens inside an electron microscope. They use electrons instead of light, because they are tiny enough to get through a really small hole

We decided question three would be the more difficult question to answer. We think that the sun's rays are the cause of this. The sun is so large that its rays travel in different directions at the top and bottom edges. Also, the position of the sun in relation to the object would affect the edges of the shadow. If the top of the flagpole is fuzzy, then the sun has reached an angle at which it is casting a shadow onto the bottom to be fuzzy.

Joe's comment:

The sun's size is the main cause of this. There is a page on the CD that shows a picture of this (the page name is sshad.htm -- change whatever it says in the "Location" window so that it ends with this).

At the flagpole edge, the shadow is sharp, but the different sun beams are going slightly different directions. The farther away you are from the thing causing the shadow, the wider is the fuzzy zone. So late in the afternoon when shadows are long, the top ends are really fuzzy.

We have totally stressed out over this trying to be perfect. If we screwed up, PLEASE correct us. Thanks.

Joe's comment:

Don't get too hung up on perfection. Right answers are nice, but the real goal is understanding and learning how to approach and discuss a problem. So these were very good answers because they made connection with what you learned and did in this section, and were explained very clearly.

(Pirates and Cardinals)

>We have completed the explore, sharp and fuzzy, shadow size and flagpole
>activites.  We were able to complete them successfully, We were a little
>confused when we discovered the computer and notebook seemed to be in a
>different order.
>
>
>
>

Joe's comment:

That's a good point. We wrote the notebook first, and then when we started writing the Virtual Workshop a different organization seemed appropriate. Since we carry the notebook around in our heads, the fact that the actual printed object is not in order didn't really occur to us.

We'll do something to fix this, and future generations of Virtual Workshop participants will have you to thank (and not know it).

> Discussion of Light and Shadows:
> This is our sure answer.  We could use a shadow to study a very small
> object.  We need a clear bulb and the object would need to be midway to the
> light source for a clear shadow.  We could only study shape not details of
> the item.  As you move closer to the light source the shape would become
> fuzzy.

We want a big shadow, greatly magnified. How big should the shadow be, with the pin halfway between light and screen?

My apologies for asking questions, but this is a nice problem, and I'm more interested in how we get to an answer than I am in the answer itself.

>
> We find ourselves unassured of this answer.  If Louise wants the picture on
> the ceiling she should use a clear bulb and small picture of the object she
> wants to show up.

>
> A Question for Joe:
> Do clear bulbs not have writing because it would show up?  Does the
> diffraction frosted bulbs cause determine why frosted bulbs do have the
> watts labeled on them? Inquiring minds in Letcher County want to know.
>

(SS)

 We 
  >have answered the questions for the section on light and shadows.  We were 
  >sure of question #2.  we know that Margie is correct that if you put the 
  >drawings directly on the bulb you won't be able to see the shadows.  You 
  >would need to place the shapes a little distance away from the bulb.

Joe's comments: What's a little distance? Did you try it (definitely allowed!). Any more advice for Louise?

  >Question #3 we think we know.  The light rays coming from the top and from 
  >the bottom of the sun are moving at a different angle than the others 
  >causing the outer edges to appear fuzzy.  The picture on the left we think 
  >is from the outer edges of the tree causing the fuzzy appearence and the 
  >picture on the right is from the middle of the tree where the shadows are 
  >clearer.

Joe's comments: The question about the tree was, why are there disks of light in the shadow? Here's a part of the picture where I see the disks very clearly: ( picture from http://www.pa.uky.edu/~sciworks/images/dapple3.jpg ) If the sun ever shines again, you can reproduce this effect even more clearly, by getting a big piece of cardboard -- 3 feet on a side, if you can find this -- and cutting a hole about 1/2" in the middle. The hole can be any shape, so why not make it square! Then have Rhonda hold up the cardboard, to make a shadow as far away as possible (easier to do around 4 PM). Mary will find the shadow has a round disk of light in the middle: why?

(Grrlz)

Least sure answer

3. We think that there is a maximum shadow size that could be produced, however we don't think the shadow would be clear enough to study. Therefore we believe that we could make a large shadow of a pin head relative to the size of the pin head itself. So the answer would be yes, going back to the premise that light travels in a straight path and the pin head will block the path of the light, therefore producing a shadow. We also know that there is a point between the screen and the light source that will produce a maximum shadow size.

Joe's comments: What point is that? As the pin gets closer to the light source, the shadow gets bigger, right? Until you bump into the light bulb or burn your fingers -- perhaps that is what you meant.

Did you try it? You will find out that it doesn't work at all! Shadows are slightly fuzzy, because the light sources have finite size. The fuzziness is unimportant if the object is large compared to the size of the light source , because the set of straight lines that can be drawn from source to object (that is, the set of light beams that will be blocked, making a shadow) is determined more by the object than by the light source. But when the object is smaller than the light source, it can't block enough of the light paths and there isn't much of a shadow (think what a bug on the screen would see, looking towards the light -- the pin is silhouetted against the light filament, and doesn't block much light).

From time to time the planets Mercury and Venus pass between the earth and the sun. These "eclipses of the sun by a planet" are not noticed at all on earth (except by astronomers that know to look for it) because there isn't any shadow -- just an imperceptible dimming of the sun's brightness.