Geometric Model, Wave Surface for a Positive Uniaxial Optical Crystal, D41,12
date: label: date made
content: ca 1900
notes: label: Description
content: This plaster model was most likely constructed in the second half of the nineteenth century in France. It is one of a set of three models (1982.0795.20, 1982.0795.22, and 1982.0795.26) representing wave surfaces of light in crystals that were probably used to teach students of optics about “double refraction,” also called “birefringence.” The wave surfaces represented by these models show the set of points that light will reach in a fixed time after emanating from a single point in a crystal. Since the speed that light travels through a crystal depends on the direction in which the light is travelling and for most directions there are two values of that speed, each wave surface has an inner and outer shell. Shells of wave surfaces that meet at four points are associated with bi-axial crystals and while those that meet at two points are associated with positive and negative uni-axial crystals. The inner and outer sheets for uni-axial crystals are a sphere and an ellipsoid with the sphere being the inner sheet when the crystal is negative.
label: Description
content: While the maker of this set of three models is not known, they resemble a set of four plaster models of octants of wave surfaces sold by Parisian optician J. G. Hofmann c. 1860. Hofmann’s models include the outer shells of both types of wave surfaces for uni-axial crystals and the inner and outer shells of the wave surface for the same bi-axial crystal. The three models of outer surfaces indicate the location of the inner shells using portions of ellipses and circles on the faces of the octants. This model corresponds to Hofmann’s model for the positive uni-axial crystal
label: Description
content: The correlation between this model and Hofmann’s model is based on the shape of the models and the lines and curves that appear on one face of the model (see AHB2016q012349.jpg) as compared with photographs of the Hofmann models from the Yale Peabody Museum of Natural History, “Plaster surface model illustrating polarization in birefringent crystal” (YPM HST.051252.A), and a slide show displaying six Hofmann models from the Teylers Museum in Haarlem, the Netherlands, “Models of wave fronts of light in birefringent crystals.” The same face that shows this model is correlated with Hoffmann’s also shows that it is a mirror image of the face on the uni-axial half of model 1982.0795.20.
label: Description
content: This model has printed inscriptions in French that match handwritten inscriptions on the Hofmann model. It also has several handwritten inscriptions including a mathematical equation involving derivatives that may have been added by the mathematics department that donated the model.
label: Location
content: Currently not on view
place: label: place made
content: Europe
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
label: See more items in
content: Science & Mathematics
creditLine: label: Credit Line
content: Gift of the Department of Mathematics, The University of Michigan
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 1982.0795.26
label: catalog number
content: 1982.0795.26
label: accession number
content: 1982.0795
objectType: label: Object Name
content: Geometric Model
physicalDescription: label: Physical Description
content: plaster (overall material)
label: Measurements
content: overall: 8 cm x 8 cm x 8 cm; 3 5/32 in x 3 5/32 in x 3 5/32 in