Question

Light Cone from a Flashlight

A flashlight is held to form a lighted area on the ground, as shown in the figure. Is it possible to angle the flashlight in such a way that the boundary of the lighted area is a parabola? Explain your answer

Short answer

Yes, the flashlight can be angled such that the ground is parallel to the slant height.

Step-by-step solution

Step 1. Given information

A flashlight is held to form a lighted area on the ground.

Step 2. Concept used

A parabola is the set of all points in a plane that has a constant distance from a fixed point, called the focus, and a fixed line called the directrix.

The cone cuts in such a way that its cross-section forms the parabola.

Step 3. Calculation

Parabola is a symmetrical figure which is a "U" shaped plane curve. It has either the lowest or highest point that is known as the vertex of the parabola.

The figure shows that the flashlight is falling on the ground.

If the cone is cut by plane such that it is parallel to the slant height of the cone, then the cross-section of the cone will be a parabola.

So, to form a parabolic boundary with the help of the flashlight angled it in such a way that the ground is parallel to the slant height of the cone.