Reflecting Property Of A Paraboloidal Mirror

Reflecting Property Of A Paraboloidal Mirror

"Mom, check out my headlight", said Tee, a sharp 7 yr old. "cool! how did you do that?", asked his mom. "Conics, just conics", replied Tee.

Explain the conic concept Tee is referring to.

The strings:

S₇P₄A₄₁ (Motion - Linear).

The math:
Pj Problem of Interest is of type motion (linear). The ray model of light implies linear motion of light.

Reflecting Property Of A paraboloidal Mirror

Conics, formally known as conic sections are curves that were originally derived from slicing a cone with a plane. The parabola, the ellipse and the hyperbola are very well known conics. The circle is also a conic section, however, its identity as a circle is dominant. Apollonius is credited with the first detailed analysis of conic sections.

Tee used the reflecting property of a parabolic mirror for his headlight. If a light source is at the focus of a parabolic mirror, the parabolic surface of the mirror will reflect all rays of light from the light source at its focus in directions parallel to the axis of the parabolic mirror. The result is a powerful beam of light concentrated in one direction.

This property is commonly used in automobile headlights which consists of a paraboloid (a paraboloid is formed by rotating a parabola about its axis) with a silvered surface so that it can reflect light and a light bulb at its focus. The light emanating from the bulb is reflected in the direction of the axis providing a concentrated beam of light in that direction (figure 21.2. where F is the focus). This property of the paraboloidal mirror is also utilised in searchlights and flashlights.

The reverse of the reflecting property of a paraboloidal mirror is also very useful. In other words, light rays parallel to the axis of a paraboloidal mirror will be reflected through the focus of the mirror. Hence there will be a high concentration of light at the focus. A telescope uses such concentration of light effectively. The axis of the telescope is directed toward the star. Since distance from star to telescope is very far, rays from the star into telecope are parallel to the axis for all practical purposes. Hence when they are incident on the surface of the paraboloid mirror of the telescope, they will be reflected to the focus of the mirror.

The reflecting property of paraboloidal mirror is also the principle used in paraboloidal reflectors which are used to concentrate radio waves emanating from a small source into a powerful beam and in paraboloidal antenna which is used to pick up faint radio signals in order to produce relatively strong signals at the focus.