Concept explainers
Reflecting Telescope The Hale telescope at the Mount Palomar Observatory has a 200-in. mirror, as shown in the figure. The mirror is constructed in a parabolic shape that collects light from the stars and focuses it at the prime focus, that is, the focus of the parabola. The mirror is 3.79 in. deep at its center. Find the focal length of this parabolic mirror, that is, the distance from the vertex to the focus.
To find: The focal length of the parabolic mirror, that is the distance from the vertex to the focus.
Answer to Problem 56E
The focal length of the parabolic mirror is
Explanation of Solution
Definition used:
“The equation of the parabola with vertex
Calculation:
From the figure observe that the parabola is open upward, hence assume the equation of the parabola be
Since the reflector is
Therefore, the point
Let the diameter passing through
Substitute
Therefore, focus of the parabolic reflector is
Therefore, the focal length of the parabolic mirror is
Chapter 11 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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