Problem Solving

4. A ray of light travels from the left to along the line x + y = 1 and reflects off the x axis. Write the equation for the reflected ray.

Solution

Draw x-y coordinate axes and sketch the ray equation x + y = 1 and the reflection off the x-axis. The reflected ray will be perpendicular to the initial ray.

The slopes of two perpendicular lines are related by: m_{1 }= -1/m_{2}.

Rewrite the first equation to see the slope of the line: y = -x + 1

The slope is -1. The slope of the second line is then: m_{2 }= -1/(-1) = 1.

We have: y = x + b

We need a data point to solve for b. Use the point where the line bounces off the x-axis.

(1, 0)

0 = 1 + b b = -1

Then: y = x – 1