The (Re)Mote in God's Eye

A couple people expressed an interest in the remote control idea, so I finished it up.

A typical remote uses modulated infrared light to send signals to a TV, or other device.  A couple questions that came to mind were: How many times can the beam bounce off the walls, and still produce a usable signal?  How long does a single command last?  How much could the signal spread out, and still be usable?

In order to answer the "usable signal" questions, we'll need to get an idea of how sensitive IR receivers are.  I couldn't find any information specifically about this, but we can at least get an upper bound on the number of bounces/signal spread by assuming that the signal power can't go below the level of the background blackbody radiation.  Warm things emit light according to a specific spectrum, called Planck's law or blackbody radiation.  The spectrum depends on the temperature of the object, and typically looks something like this (from Wikipedia):

At room temperature (300 K), the infrared power emitted is about 1.2 x 10^-14 W/m^2.  According to this site, a smallish living room is about 14 m^2, meaning the total surface area of the walls, floor, and ceiling for a square room is 65.5 m^2.  Multiplying by the power density we found above, we get 7.8 x 10^-13 W.  Not very much, but like I said, we're getting an upper bound.

To answer the question about bounces, we need to know how reflective the walls are.  It turns out that paints actually specify a property called LRV, or light reflectance value.  Typical white paint has an LRV of 85, meaning it reflects about 85% of the light that hits it.  After n bounces then, the light power will be

where Pe is the emitted power.  Normal LEDs emit about 30 mW of power, so we have

or n = 150, a fair number of bounces, but certainly not unreasonable.

The question about spread can be answered by considering how large the beam becomes as it leaves the remote.  If the LED's viewing angle is θ, after a distance d the spot size will be

The amount of power received then will be

where a is the area of the receiving LED.  Typical LEDs have a diameter of 5 mm, and wide-angle LEDs have a viewing angle of 100°.  Plugging these values in, and solving for d, we find d = 86.5 meters.

I couldn't find information on the timing of commands, but at least now Nate can proceed with his stealth channel changing operations.