Jantar Mantar: The Science of Indian Conjecture

Every hour, the shadow on the gnomon moves approximately 4 metres. This translates
to 6 cm every minute and, with each minute sub-divided into thirty fractions, the sundial is
theoretically able to provide a remarkable accuracy of 2 seconds. The bona fide precision,
however, differs in accordance with the sceptical eye, with claims ranging from half a second to
as far wide as half a minute.
Instrument inaccuracies: the conundrum of shade diffraction
The premise behind such broad estimates is not unfounded. In the quest for accuracy
through size, the designers had perhaps overlooked one fundamental flaw – that of shade
diffraction. The volume of the shadow cast behind any object illuminated by an area light source
Light
Source
Object
penumbra
umbra
penumbra
Fig. 3
does not possess clearly defined boundaries. Every point within the boundary area is instead in
partial shadow. The area of full shadow is known as the umbra, and the area of partial shadow
is termed the penumbra. (See Fig. 3) Note that the diagram is only an approximation, since the
penumbra is characterised by a shadow-light gradient rather than homogenous shadow density.
In the context of the large sundial, the area light source is the sun. By nature of its great
distance from our planet, the sun emits light rays which may be taken to be parallel upon
reaching earth. This is in contrast with a point source emanating rays which originate and
32
J M