5.7.4 Reflective property of parabola

The light or sound or radio waves originating at a parabola’s focus are reflected parallel to the parabola’s axis (Fig. . ) and conversely the rays arriving parallel to the axis are directed towards the focus (Fig. .

). Example . The equation y = models cross sections of parabolic mirrors that are used for solar energy. There is a heating tube located at the focus of each parabola; how high is this tube located above the vertex of the parabola?

Equation of the parabola is y = x That is x = y ; the vertex is ( , ) = ( ) y ⇒ a = So the heating tube needs to be placed at focus ( , ) a . Hence the heating tube needs to be placed units above the vertex of the parabola. Example . A search light has a parabolic reflector (has a cross section that forms a ‘bowl’).

The parabolic bowl is cm wide from rim to rim and cm deep. The bulb is located at the focus . ( ) What is the equation of the parabola used for reflector? ( ) How far from the vertex is the bulb to be placed so that the maximum distance covered?