1.5 would require the exposure to be extended to 6 seconds for the same result. Reciprocity failure generally becomes significant at exposures of longer than about 1 sec for film, and above 30 sec for paper. Reciprocity also breaks down at extremely high levels of illumination with very short exposures. This is a concern for scientific and technical photography, but rarely to general photographers, as exposures significantly shorter than a millisecond are only required for subjects such as explosions and in particle physics, or when taking high-speed motion pictures with very high shutter speeds (1/10,000 sec or faster). Schwarzschild law In response to astronomical observations of low intensity reciprocity failure, Karl Schwarzschild wrote (circa 1900): "In determinations of stellar brightness by the photographic method I have recently been able to confirm once more the existence of such deviations, and to follow them up in a quantitative way, and to express them in the following rule, which should replace the law of reciprocity: Sources of light of different intensity I cause the same degree of blackening under different exposures t if the products are equal." Unfortunately, Schwarzschild's empirically determined 0.86 coefficient turned out to be of limited usefulness. A modern formulation of Schwarzschild's law is given as where E is a measure of the "effect of the exposure" that leads to changes in the opacity of the photosensitive material (in the same degree that an equal value of exposure H = It does in the reciprocity region), I is illuminance, t is exposure duration and p is the Schwarzschild coefficient. However, a constant value for p remains elusive, and has not replaced the need for more realistic models or empirical sensitometric data in critical applications. When reciprocity holds, Schwarzschild's law uses p = 1.0. Since the Schwarzschild's law formula gives unreasonable values for times in the region where reciprocity holds, a modified formula has been found that fits better across a wider range of exposure times. The modification is in terms of a factor the multiplies the ISO film speed: Relative film speed where the t + 1 term implies a breakpoint near 1 second separating the region where reciprocity holds from the region where it fails. Simple model for t > 1 second Some models of microscope use automatic electronic models for reciprocity failure compensation, generally of a form for correct time, Tc, expressible as a power law of metered