Using ideas from Optics, Physics, and Romulan Star Trek scifi technology, Humanoido at SPACE1 has invented the CLASSIFIED cloaking device for starships. The derivation of Snell's Law from optics and physics predicts degrees of invisibility. (see ray tracing figure) Romulans of scifi Star Trek used the above configuration for a cloaking device. However, SPACE1 is adopting optics which itself is transparent.
by Humanoido
The Cloak provides an optical and electromagnetic radiation invisibility shield to spacecraft flown as starships. The shield is physically implemented and the craft maintains a specific calculated orientation to the line of invisibility when the cloak is brought online. The starship hull contains the cloak material from which it's lined. The SPACE1 starship cloak optically refracts light around the starship creating a cloak of invisibility. More testing of the Cloak is needed in hot and cold environments, as the working prototype is operating across room temperature and end to end extremes.
Formulae derivation is from a Computer Math program I wrote at the University and is based on both the derivation and real time implementation of Snell's Law, with graphical representation, on an IBM mainframe computer. In its simplest form, Snell's law can be derived from Fermat's principle, which states that the light travels the path which takes the least time. By taking the derivative of the optical path length, the stationary point is found giving the path taken by the light.
Deriving a working example of Snell's law for a stealth cloaking device, light from medium 1, point Q, enters medium 2, refraction occurs, and reaches point P finally. Assume the refractive index of medium 1 and medium 2 are {\displaystyle n_{1}}n_{1} and {\displaystyle n_{2}}n_{2} respectively. Light enters medium 2 from medium 1 via point O. {\displaystyle \theta _{1}}\theta _{1} is the angle of incidence, {\displaystyle \theta _{2}}\theta _{2} is the angle of refraction with respect to the normal. The phase velocities of light in medium 1 and medium 2 are v_1=c/n_1 and {\displaystyle v_{2}=c/n_{2}}v_2=c/n_2 respectively.
{\displaystyle c}c is the speed of light in vacuum. Let T be the time required for the light to travel from point Q through point O to point P.
{\displaystyle T={\frac {\sqrt {x^{2}+a^{2}}}{v_{1}}}+{\frac {\sqrt {b^{2}+(l-x)^{2}}}{v_{2}}}={\frac {\sqrt {x^{2}+a^{2}}}{v_{1}}}+{\frac {\sqrt {b^{2}+l^{2}-2lx+x^{2}}}{v_{2}}}}{\displaystyle T={\frac {\sqrt {x^{2}+a^{2}}}{v_{1}}}+{\frac {\sqrt {b^{2}+(l-x)^{2}}}{v_{2}}}={\frac {\sqrt {x^{2}+a^{2}}}{v_{1}}}+{\frac {\sqrt {b^{2}+l^{2}-2lx+x^{2}}}{v_{2}}}} where a, b, l and x are as denoted in the long derivation, x being the varying parameter.
To minimize it, one can differentiate:
\frac{dT}{dx}=\frac{x}{v_1\sqrt{x^2 + a^2}} + \frac{ - (l - x)}{v_2\sqrt{(l-x)^2 + b^2}}=0 (stationary point). Note that {\displaystyle {\frac {x}{\sqrt {x^{2}+a^{2}}}}=\sin \theta _{1}}\frac{x}{\sqrt{x^2 + a^2}} =\sin\theta_1
and {\displaystyle {\frac {l-x}{\sqrt {(l-x)^{2}+b^{2}}}}=\sin \theta _{2}}\frac{ l - x}{\sqrt{(l-x)^2 + b^2}}=\sin\theta_2. Therefore,
{\displaystyle {\frac {dT}{dx}}={\frac {\sin \theta _{1}}{v_{1}}}-{\frac {\sin \theta _{2}}{v_{2}}}=0}\frac{dT}{dx}=\frac{\sin\theta_1}{v_1} - \frac{\sin\theta_2}{v_2}=0
{\displaystyle {\frac {\sin \theta _{1}}{v_{1}}}={\frac {\sin \theta _{2}}{v_{2}}}}{\displaystyle {\frac {\sin \theta _{1}}{v_{1}}}={\frac {\sin \theta _{2}}{v_{2}}}}
{\displaystyle {\frac {n_{1}\sin \theta _{1}}{c}}={\frac {n_{2}\sin \theta _{2}}{c}}}\frac{n_1\sin\theta_1}{c}=\frac{n_2\sin\theta_2}{c}
{\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}}n_1\sin\theta_1=n_2\sin\theta_2
The Cloak will be installed on the hull of the super spacecraft or super starship version of the Super Rocket. SPACE1 has completed a transporter and is working on shields, phasers, and photon torpedos. The Cloak will allow SPACE1 to work and perform starship experiments in space without drawing significant attention.
