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Blue sky is a product of sunlight Rayleigh scattered by air molecules. Its light is preferentially polarised with the electric vector perpendicular to the sun's rays and the polarisation is almost complete at 90º from the sun. Analysis of the polarisation gives the sun direction and so any device that splits blue skylight light into two polarised components and compares their intensities can act as a sunstone or sun seeker.
An Iceland Spar, calcite, crystal is just such a device. The crystal, built of arrays of negatively charged carbonate and positive calcium ions, is highly anisotropic. Light entering the crystal splits into two polarised components which travel in different directions. It is 'doubly refracting' and objects viewed through it appear doubled.
Look straight down on a rhombus shaped calcite crystal (mineral specimen stores often have them) and an object beneath it is seen double. Rotate the crystal. One image stays nearly stationary and the other (the one farthest from the top blunt corner) moves around it. Calcite is 'birefringent' or 'double refracting'.
Calcite is a crystalline form of calcium carbonate, CaCO3, and the crystal is a lattice of positively charged calcium and negatively charged carbonate ions. The very large optical effects shown by calcite arise because the flat carbonate ions are arranged in parallel sheets. Light travelling perpendicular or parallel to them has very different electronic interactions. The crystal is anisotropic and its optical properties are direction dependent.
Light entering the crystal splits into two polarised components because the differently oriented electric vectors of the radiation interact differently with the induced dipoles of the carbonate oxygen.
One ray, called the ordinary or O ray, behaves in the familiar way of light passing through glass or water (as predicted by Snell's law of refraction). The second - the extraordinary or E ray - is indeed extraordinary, it is refracted through a different angle to the O ray. Worse, Snell's Law does not predict the refraction because its extent, given by the refractive index, is direction dependent.
Below, the upper unpolarised view shows the double image. In the lower views a plane polarising camera filter is rotated to reveal one or other of the polarised images.
All non-cubic symmetry crystals (calcite is trigonal, common salt is cubic as also is diamond) are birefringent but often only to an unnoticeably small degree. Ice (hexagonal symmetry) is birefringent enough that a carefully rotated polarising filter shows the presence of doubly imaged sundogs
The O and E rays passing through thin sheets of birefringent materials have different optical path lengths. The rays interfere giving the coloured bands that are often seen when looking through airplane windows.
Place a paper sticker, or blob of Viking Stockholm tar, on the crystal top face and as seen through the bottom face it is doubled. Hold the crystal to the sky with its upper face level and rotate it to and fro. The two images change in intensity. When they are equally dark - a condition that can be judged rather precisely - the crystal long edges point in the sun's direction.
To be effective the sun must be low - as needed anyway for the Viking horizon board - with moderately blue sky overhead. The sun seeker does not work on completely cloudy days because any light from blue sky beyond them is depolarised by multiple scattering from the cloud water droplets.
Test the operation of a sunstone on cloudy days by looking through it at a white LCD monitor screen (strongly polarised). As the crystal is rotated the two images change in intensity.
The Vikings started to settle in Iceland in the 860-70s. Inhabitable land was eventually taken and the Icelandic Sagas have it that a new land, Greenland, was reconnoitred in the 980s by Eric the Red. Two colonies of 3-4000 people were later established on its western coast. North America was probably first sighted by Bjarni Herjolfsson who, driven off course in 985/6 en route to Greenland from Iceland, reached but did not set foot on land to the west. Erik the Red's son, Leif the Fortunate, made a deliberate voyage westwards in ~1001, crossed the Davis Straight and landed on Baffin Island. He then sailed down the coast of Labrador to Newfoundland where a Viking settlement has been discovered. It is uncertain whether he sailed further south although vines and grapes were said to have been found and the Vikings called the land Vinland. From then on Viking longships regularly sailed back and forth across the Atlantic.
The Vikings were remarkable seafarers. There is no evidence that they had a magnetic compass. With our almost total reliance on advanced electronics and satellites for navigation it is seen as near impossible that Vikings in their small open ships could make such voyages without some navigational device. Their voyages were made in summer and at high latitudes the days were long and the sky did not get completely dark. Celestially, they had to rely on the sun rather than stars.
There is some evidence that they used an horizon board to help find latitude. This had the bearing of the sunrise and sunset marked with peg holes for their home port and a number of dates. To sail due west and reach Iceland and then Greenland they could sight the sun at sunrise and sunset each day and compare it with pegs on the board to set their course west.
However, the North Atlantic especially in Arctic or near Arctic waters is frequently cloud covered or there is a sea fog layer that hides a low sun but irritatingly shows blue sky overhead - thus the need for a sun seeker. On a typical Arctic morning with thin fog hiding sunrise an Iceland Spar sunstone could easily give an accurate bearing. Similarly towards sunset when distant clouds often hide the sun but leave some blue sky overhead the sunstone also works. And Iceland Spar crystals could be found on the ground in Iceland.
This is speculation, there is no direct evidence that they used sunstones. Less exciting perhaps, they were simply consummate sailors. The smells of the air and of the ocean, the character of the waves and winds, birds and moods of the sky were all cues that they were likely very sensitive to. They perchance had little need of magical devices.