Question 8
Context: Observe what happens to the size of the shadow as you vary the distance between your torch and your object.
Q. Why does this happen?
- A shadow is formed when an opaque object blocks light rays traveling from a light source (the torch) to a screen.
- Light rays diverge (spread outward) in straight lines from the torch.
- Varying the distance between the torch and the object changes the angle of the diverging light rays blocked by the object, thereby changing the size of the shadow cast on the screen.
Step 1 · Observation of Shadow Size
When observing the shadow on a screen:
- Moving the torch closer to the object makes the shadow larger.
- Moving the torch farther from the object makes the shadow smaller.
Step 2 · Explanation Using Diverging Light Rays
Light rays spread out in all directions from the torch forming a cone:
- When the torch is closer to the object, the light rays spread out at a wider angle as they reach the object. The object intercepts a wider cross-section of the light beam, casting a larger shadow on the screen.
- When the torch is farther from the object, the rays hitting the edges of the object spread out less sharply, casting a smaller shadow on the screen.
When the torch is closer to the object, the diverging light rays are intercepted at a wider angle, producing a larger shadow. When the torch is moved farther away, the angle of divergence at the object is smaller, producing a smaller shadow.
- Inverting the Distance Relationship: Thinking that bringing the light source closer makes the shadow smaller. In reality, moving the source closer increases the angle of divergence and makes the shadow larger.
- Confusing Light-to-Object with Object-to-Screen Distance: Moving the torch closer to the object increases shadow size, whereas moving the object closer to the screen decreases shadow size.
More questions in A
Build it in Your Imagination
We will start this section by practising visualisation. For each prompt, feel free to talk to your partner, gesture, draw it in the air — but do not actually draw on paper!
- Picture your name, then read off the letters backwards. Make sure to do this by sight, not by sound — really see your name! Now try with your friend's name.
Cut off the four corners of an imaginary square, with each cut going between midpoints of adjacent edges. What shape is left over? How can you reassemble the four corners to make another square?
Mark the sides of an equilateral triangle into thirds. Cut off each corner of the triangle, as far as the marks. What shape do you get?
Mark the sides of a square into thirds and cut off each of its corners as far as the marks. What shape is left?
Net of a sphere? Experiment and see if you can make a paper cutout that can perfectly wrap around a ball without leaving any wrinkles, gaps or overlaps.
Place an object in front of a plane, such as a wall of your room. Shine a torch light on the object in a direction perpendicular to the wall.
What do you see?
Observe what happens to the size of the shadow as you vary the distance between your torch and your object.
Context: Observe what happens to the size of the shadow as you vary the distance between your torch and your object.
Q. Why does this happen?
Construct a model of a cube and use your hands to keep it balanced on one corner vertex. Can you try to understand why all the projected edges have equal length?