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on the 7 strands

Scientific
activities

 Geometrical
activities		 Quadrilaterals Geometrical
transformations

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 CABRI files

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Fractals

SHADOWS PRODUCED BY A NEAR LIGHT SOURCE

The model of the “light rays” allows to explore the formation of the shadows . The strings connecting corresponding points between the ball and the shadow join at the lamp.
If we project a solid object we can see a shadow and a half-light zone, while if we project a bidimensional figure, the outline of the shadow is more defined.

Source: slides projector

Source: slides projector

An exercise is to predict the position and shape of the shadow on the screen. Pupils have to stretch strings from the lamp to the screen and passing through the object, when the lamp is turned off, then draw the “virtual shadow” on the screen.
Later they verify that the “real shadow” coincides with the drawn outline.

Then students explore how the lamp position, the screen position and the object position influence the shadow shape and size. More in details:

Frame plane not parallel to the screen plane

Source: slides projector

Source: table lamp
  • Shape and dimensions change, the square becomes a trapezium.
  • Only the side on the screen (or on the floor) remains unchanged.
  • Straight lines remain straight.

But not always straight lines remain straight. See below whay happens if we use a curve surface:

Frame plane parallel to the screen plane
  • The shadow keeps its shape.
  • If the relative distance between the source, frame and screen is changed, the size of the shadow changes.

Students are asked to predict at what distance the frame has to be put between the fixed screen and the projector to create a chosen enlargement. This activity helps the development of proportional thinking.

CABRI offers a rich environment to study the enlargement from a mathematical point of view.

Cabri file | CabriJava

WHAT HAPPENS IF YOU MOVE AWAY THE LIGHT SOURCE?

If you move away the projector, keeping in the same position the screen and the frame, you can observe that:

  • The shadow reduces itself; the students easily predict that, at an infinite distance, shadow and frame would have the same size.
  • The strings connecting two points of the frame with the lamp and representing the “light rays” keep longer their distance. If the lamp were at infinite distance, they would be parallel.

In this way the idea of shadows produced by a far source is spontaneously introduced.

Geometrical transformations and shadows | Shadows produced by the sun

 

 
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