than differential elements), and which are separated by a medium of refractive index n that is perfectly transparent (shown). To compute the etendue of the system, one must consider the contribution of each point on the surface of the light source as they cast rays to each point on the receiver. According to the definition above, the etendue of the light crossing dΣ towards dS is given by: where dΩΣ is the solid angle defined by area dS at area dΣ, and d is the distance between the two areas. Similarly, the etendue of the light crossing dS coming from dΣ is given by: where dΩS is the solid angle defined by area dΣ. These expressions result in showing that etendue is conserved as light propagates in free space. The etendue of the whole system is then: If both surfaces dΣ and dS are immersed in air (or in vacuum), and the expression above for the etendue may be written as where FdΣ→dS is the view factor between differential surfaces dΣ and dS. Integration on dΣ and dS results in G = πΣ FΣ→S which allows the etendue between two surfaces to be obtained from the view factors between those surfaces, as provided in a list of view factors for specific geometry cases or in several heat transfer textbooks. Conservation of etendue The etendue of a given bundle of light is conserved: etendue can be increased, but not decreased in any optical system. This means that any system that concentrates light from some source onto a smaller area must always increase the solid angle of incidence (that is, the area of the sky that the source subtends). For example, a magnifying glass can increase the intensity of sunlight onto a small spot, but does so because, viewed from the spot that the light is concentrated onto, the apparent size of the sun is increased proportional to the concentration. As shown below, etendue is conserved as light travels through free space and at refractions or reflections. It is then also conserved as light travels through optical systems where it undergoes perfect reflections or refractions. However, if light was to hit, say, a diffuser, its solid angle would increase, increasing the etendue. Etendue can then remain constant or it can increase as light propagates through an optic, but it cannot decrease. This is a direct result of the fact that entropy must