Shadows as Projections

Transcript

Shadows as Projections UNDERSTANDING SHADOWS AS PROJECTIONS: FROM FLASHLIGHTS TO THE SUN CLOSE LIGHT SOURCE (e.g., Flashlight)1. Shadows as "Projections" Imagine taking a 3D object and squishing it completely flat against a wall. That flat 2D shape is called a projection. In the picture, a flashlight is shining on a 3D cylinder. Even though the object is round, the shadow it casts on the flat wall is a rectangle! The shadow is acting like a projection of the cylinder. 2. The Flashlight Experiment (Close-up Light) The book asks: Observe what happens to the size of the shadow as you vary the distance between your torch and your object. If you hold a flashlight close to an object, the light rays spread out like a fan. Because the rays are spreading outwards, they make the shadow on the wall look bigger than the actual object. If you move the flashlight further back, the shadow shrinks. move the flashlight further back, the shadow shrinks. 3. The "Imaginary Torch" (The Sun) The book then asks you to imagine a super powerful flashlight that is incredibly far away. When a light source is that far away, the light rays don't hit the object at wide angles anymore. By the time they reach the object, the rays are traveling in perfectly straight, parallel lines. You experience this every day with the Sun! Because the Sun's rays are parallel, they don't stretch or magnify the shadow. The shadow becomes an exact, perfect 2D projection of the object. 4. The Golden Rule of Parallel Lines The blue box at the bottom shares a special rule in geometry: "More generally, the projection of a pair of parallel lines will always remain parallel." If you cut out a shape that has parallel sides (like a square, rectangle, or parallelogram) and look at its shadow under the Sun, the lines of the shadow will also be parallel. Even if you tilt or spin the shape, the shadow might stretch into a different shape, but those parallel sides will never cross each other. Summary This page is teaching you that shadows made by the Sun are special because the light rays are parallel, meaning they create perfect geometric projections where parallel lines always stay parallel!