Answer
The reflection of the light will appear 10 feet from the buoy on the water's surface, considering the observer's position and the angle of reflection.
Work Step by Step
For reflection in a flat surface (like still water), the angle of incidence = angle of reflection.
We can solve this geometrically by imagining a mirror image of the light below the water.
Let’s place a coordinate system:
Water surface along the x-axis.
The buoy (light) is at (0,10).
The mirror image of the light is at (0,−10).
The observer’s eyes are at (15,5).
Then the line of sight from the observer to the image of the light gives the apparent reflection point on the water.
Find where the line from the observer to the image intersects the water surface
The image of the light is at (0,−10).
The observer is at (15,5).
We find the equation of the line joining them.
$y-y_1=m(x-x_1)$
where
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-10-15}{0-15}=1$
Equation of the line is:
$y=x-10$
Find where this line meets the water surface (y=0):
$0=x-10\Rightarrow x=10$
The reflection of the light will appear 10 feet from the buoy on the water's surface, considering the observer's position and the angle of reflection.
