Illuminations: Light Bounce

Light Bounce
This tool allows you to investigate the new Light It Up game at the Springfield Fair. The game involves aiming a laser pointer from a height of 150 cm at a mirror (M) that is 10 cm off the ground and 25 cm from the wall. The goal is to make the reflection of the beam (R) reach a height of exactly 1 m up the wall. The difficulty is determining the proper distance from the wall at which to place the pointer (P).

Instructions
 
Use the three red dots on the screen to adjust the parameters for this investigation. The parameters are the vertical height of the flashlight, the distance of the mirror from the wall, and the distance of the flashlight (P) from the wall. (Note that the mirror is 10 cm off the ground.)

Drag point P back and forth along the horizontal gray line. As P moves, the reflection off of a mirror (M) will reach a point on the wall (R).

Exploration
 
Drag the red dots to adjust the parameters for this investigation so that Distance from Pointer (P) to Floor = 150 and Distance from the Mirror (M) to Wall = 25. At what distance (P) should the laser pointer be located so that the reflection (R) reaches a height of exactly 1 m?

 

In general, what is the relationship between the height of the reflection (R) and the distance from the pointer (P) to the wall?

  • Collect data to determine the relationship.
  • What algebraic rule can be used to determine the location of the laser pointer when the height of the reflection is known?

  
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NCTM Resources

Navigating through Algebra in 9‑12

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