A parabolic reflector for a car headlight forms a bowl shape that is wide at its opening and deep, as shown in the figure at the left. How far from the vertex should the filament of the bulb be placed if it is to be located at the focus?
The focal point of the parabolic reflector for a car headlight which forms a bowl shape.
The bowl shape parabolic reflector for a car headlight is wide at its opening and deep.
Introduce a coordinate system and place parabolic reflector in the system such that its vertex is at the origin and wide side towards the positive -axis.
Place parabolic reflector in the coordinate system, such that its vertex is at the origin in the positive -axis, as shown below in the figure. Then the equation of the parabola looks like,
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