Mirror Mirage

Age

Elementary School, Middle School, High School

Format

Hands-on

Materials

   Mirage toy, consisting of two parabolic mirrors
   An object to stick in the mirage toy such as a quarter or dice. 

Safety Precautions

Science Theatre demonstrators must keep the safety of themselves and their audience in mind at all times. All Science Theatre demonstrators must have read through the Safety Training page. The ST Safety Box with first aid kit, fire extinguisher, etc. should always be available to demonstrators. Always wear safety gloves, glasses, and a labcoat if handling chemicals; always perform potentially dangerous demonstrations at a safe distance from the audience; and always keep a very close eye on any volunteers you call from the audience.

Preparation

Simply place the parabolic mirror with the hole in the center on top of the parabolic mirror with no hole.

Demonstration

Insert an object at the focus of the bottom mirror (simply at its center). A real image of the object will then appear at the focus of the second mirror, easily visible from an angle.

What to Say

This is a very simple demonstration, but it teaches several interesting concepts in geometrical optics.

Reproduce the diagram to help students understand that:

Light naturally spreads out spherically (in all directions); for instance, light from the object you place in the mirror will spread out in all directions. In each direction, we say that a "ray" of light is travelling in a straight line. For older audiences, you may want to introduce the photon concept.

Rays of light reflect off of shiny surfaces such as mirrors. Reflected rays bounce off the surface at the same angle at which they hit it. In other words, a ray of light that hits a surface head on will be reflected right back and a ray that hits the surface at a large angle will bounce off at a large angle.

Parabolic mirrors have a special shape. Objects at their center are in their "focus." Light from these objects heads out in all directions, but, in every direction, they hit the mirror at such an angle that they bounce off going straight up in parallel.

Using two parabolic mirrors, we can refocus those parallel rays! The object is placed at the focus of the top mirror. Parallel rays are then sent to the bottom mirror, which focuses those rays at the hole in the top mirror.

Some questions you could ask:

You can easily see the real image at an angle. How come you don't see two objects (the object and its image) when you look straight down? The reason is that no rays reflected by the mirror will reach your eye when it is positioned directly above the object. Only rays emitted by the object itself can go straight up to your eye! Reproduce the diagrams to help students understand the path the light travels in.

Why It Is

Light is always reflected from a surface at the same angle at which it is incident. In other words, a ray of light that hits a mirror at 30 degrees relative to the normal (the normal is a line perpendicular to the mirror) will be reflect at 30 degrees on the other side of the normal.

A parabolic mirror is in the shape of a parabola rotated around an axis. This shape is special in that rays emitted at its center (its focus) will always reach the side of the mirror at such an angle that they are reflected straight away from the mirror. In other words, all the light from an object at the focus of the mirror will exit the mirror collimated - the rays will be parallel.

The mirage mirror toy then uses a second parabolic mirror to converge those parallel rays back into a real image at the focus of the second mirror. The object is placed at the focus of the top mirror (which is located at the center of the bottom mirror). The focus of the bottom mirror is where the image is formed: at the hole in the top mirror. The image is real, upright, and at a magnificiation of 1, so it looks exactly like the original object!

Real Life Examples

The property of parabolic mirrors that they produce collimated rays from an object at their focus is useful in many applications:

Car headlights - your headlights appear brighter if you can collimate them and focus the light in one direction, rather than spreading out in all directions.

Directional speakers - these use special "mirrors" that reflect sound waves out in only one direction (as parallel rays).

The inverse also holds - rays entering the parabolic mirror in parallel (as from an object very far away) converge at the mirror's focus. This is useful in a variety of applications:

Satellite dishes Directional microphones - these only focus sound coming from one direction, so you can filter out ambient noise. Astronomical telescopes - mirrors have a big advantage over lenses that they do not suffer from chromatic aberattion.