To find: How deep should the mirror be in order to reflect the light rays parallel to the axis of symmetry.
Answer to Problem 39RE
Depth of the mirror should be feet or 3 inches.
Explanation of Solution
Given:
A searchlight is shaped like a paraboloid of revolution. If a light source is located 1 foot from the vertex along the axis of symmetry and the opening is 2 feet across.
Calculation:
Let be the vertex of the parabola and let it open up.
The equation of the parabola is .
The light source is located 1 foot from the vertex along the axis of symmetry.
Therefore, .
Hence, the equation is .
The width of opening is 2 so that is located on the parabola.
Substituting in , we get,
,
feet
The mirror is feet, or 3 inches.
Chapter 10 Solutions
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