How deep should the mirror be in order to reflect the light rays parallel to the axis of symmetry?
Answer to Problem 77RE
The light bulb should be placed
Explanation of Solution
Given information:
A searchlight is shaped like a paraboloid of revolution. If a light source is located
Calculation:
Since, the rays are to be reflected parallel to the axis of symmetry, the light bulb should be placed at the focus of the parabola.
Given that the searchlight is in the shape of paraboloid of revolution with width
Since, the width is
The equation of such a parabola is given by
Since, we have the point
Now, divide both sides by
Thus, the focus is at
Hence, the light bulb should be placed
Chapter 10 Solutions
Precalculus
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