Relativistic Doppler effect invisible ultraviolet wavelengths, infrared light is blueshifted into the visible range. Precisely what changes in the colors one sees depends on the physiology of the human eye and on the spectral characteristics of the light sources being observed. The Doppler effect (with arbitrary direction) also modifies the perceived source intensity: this can be expressed concisely by the fact that source strength divided by the cube of the frequency is a Lorentz invariant This implies that the total radiant intensity (summing over all frequencies) is multiplied by the fourth power of the Doppler factor for frequency. As a consequence, since Planck's
Invisible ink writing with soap water may be made visible either by heat, reaction with phenolphthalein, viewing under ultraviolet light, or by placing the page inside an iodine fume cupboard. Some of these are organic substances that oxidize when heated, which usually turns them brown. For this type of "heat fixed" ink, any acidic fluid will work. The most secure way to use any of the following substances for invisible ink is by dilution, usually with water, close to the point when they become difficult to develop. The writing is rendered visible by heating the paper, either on a radiator, by ironing