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 purpose stylus, stamp, fountain pen, toothpick, calligraphy pen, or even a finger dipped in the liquid. Once dry, the written surface looks as if it were blank, with a similar texture and reflectivity as the surrounding surface. The ink can be later made visible by different methods according to the type of invisible ink used. The ink may be revealed by heat or by application of an appropriate chemical, or it may be made visible by viewing under ultraviolet light. Inks which are developed by a chemical reaction may depend on an acid-base reaction (like litmus paper), reactions similar to