Question

Which of the following are real life examples of reflective property of a parabola?
A.Satellite dish
B.Headlight
C.Fountains
D.Plane mirror

Answer 1

Here, we will first use the definition of the reflective property of a parabola. Then we will analyze each option whether they satisfy the condition of reflectivity of a parabola. The options that satisfy the condition are the correct answer.

Complete step-by-step answer:
The reflective property of parabola is that when a ray coming from the positive $x$-axis reflects back it passes through the focus of the parabola and similarly if a ray of light is passing through the focus it will reflect off in a line parallel to the $x$-axis.
Now, we will observe each option and find out which option satisfies the reflective property of the parabola.
A satellite dish collects all the electromagnetic rays in one point which helps in obtaining a strong signal.
A headlight uses the same concept but in the opposite way here the light emitted from the headlight gets focused in one point as a beam so that it doesn’t scatter away in a different direction.
In both Satellite and headlight, the cross-section is in parabolic shape so that the emission points act as a focus for the parabolic shape.
A fountain doesn’t use this property as in this the pump forces the water upward to create a falling view. It forms a parabolic path but not the reflective property of the parabola is satisfied.
In a plane mirror, the angle of reflection is equal to the angle of incidence so when light falls on it, it is directly reflected back on the same path.
Now we can conclude that only the satellite dish and headlight satisfies the reflective property of the parabola.
Therefore, option (A) and (B) is correct.

Note: Parabola is a conic shape that is mirror-symmetrical. Some important use of the reflective property of a parabola is:
To direct radio waves we use the parabolic antenna for point-to-point conversation.
Some heaters also use this property where they focus the heat source at one point and emit the heat in parallel rays in all directions.