Constructing a Flashlight The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 4 inches and its depth is 1 inch. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?
Constructing a Flashlight The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 4 inches and its depth is 1 inch. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?
Constructing a Flashlight The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 4 inches and its depth is 1 inch. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?
Expert Solution & Answer
To determine
To find: How far from the vertex should the light bulb be placed, if the diameter is 4 inches and its depth is 1 inch, so that the rays will be reflected parallel to the axis?
Answer to Problem 65AYU
Light bulb should be placed 1 inch from the vertex.
Explanation of Solution
Given:
The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 4 inches and its depth is 1 inch.
Formula used:
Vertex
Focus
Directrix
Equation
Description
Parabola, axis of symmetry is , opens up.
Calculation:
Let the vertex of the parabola be and let it open up.
The equation of the parabola is given by where is the distance from vertex to focus.
The parabola is 4 feet across at its opening and 1 feet deep.
The points
and are the points on the parabola.
Substituting the points in the equation , we get,
inch.
The light bulb should be placed 1 inch from the vertex so that the rays will be reflected parallel to the axis.
Thomas' Calculus: Early Transcendentals (14th Edition)
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