Art. XLV.—An Experiment bearing on the Wave Theory of Light.

Transactions and Proceedings of the Royal Society of New Zealand, Volume 36, 1903, Page 487

Art. XLV.—An Experiment bearing on the Wave Theory of Light. By J. S. S. Cooper, M.A., B.Sc. [Read before the Otago Institute, 9th June, 1903.] 1. Theory. Consider a parallel plate of some transparent medium whose refractive index varies as the distance of the point from an initial plane at right angles to the face of the plate. Let light from a distant source (a plane wave) be incident normally on this plate. The wave theory indicates that there will be a deviation.

Let the thickness of the slab be t, and let a small element of the wave-front be AB (fig. 1), measured parallel to the Fig. 1. plate, but at right angles to the initial plane. Let this wave emerge from the plate at CD, and let its front be now DM, making an angle δ with the face of the plate. Let the refractive index along CD be μ, and that along AB be μ1. The plate is supposed immersed in air of refractive index unity. We may consider the element DM to be plane. Let AB = x; Then time taken to travel path BD = kμt; Time taken to travel path AM = kμ1t + kCM. Whence BM = μt - μ1t. ∴ Sin δ = BM/BD = μt - μ1t/x, if we neglect internal refractions From this it follows that, in order that the wave may remain plane, we must have dμ/dx = constant (= λ). Then the deviation δ is given by Sin δ = λt. Or, if δ is small, δ varies as t…… …(1.) 2. Experiment.(Fig. 2.) In order to test; this experimentally the prisms were removed from a spectrometer, which was then fixed with its

graduated circle vertical and its collimator-tube horizontal. A small glass tank with approximately parallel sides was now placed at the centre of the circle, and the deviation it produced was noted. The tank was now half-filled wish gasoline, and carbon-bisulphide was run in underneath by means of a funnel. In the region where they mix we have then a liquid slab fulfilling the conditions stated in the first Fig. 2. Diagrammatic Plan, op Spectrometer. a a Region of mixture. sentence of this paper. These liquids mix freely in all proportions without turbidity. The beam now passed through the mixture-layer, and the deviation was noted. At the same time a notable dispersion was observed. It then occurred to the author that these effects might be produced by prisms formed by capillary attraction in contact with the glass sides of the tank. If this were so, the introduction of a glass slip (a microscope-slide) would make four such prisms instead of two, thus doubling the deflection. A microscope-slide was carefully introduced in a vertical position, and the observed deflection was sensibly diminished. The introduction of another slab caused a further reduction of the deviation which was in sensible proportion to the thickness of the liquid traversed. On now mixing the liquids thoroughly there was only such deviation as was accountable by the inclination of the sides of the tank, and that in a contrary direction to the previous, deviations. There was no prismatic dispersion observable. Details of One of the Experiments. Deviation produced by glass sides of empty tank = - 10′ " by tank with gasoline = - 1′ " by region of mixture (t = 7.5mm.) = + 62′ " with microscope-slip 2 mm. in thickness (t = 5.5mm.) = + 44′

Deviation produced with microscope-slip 1–6 mm. in thickness (t = 5.9 mm.) = + 47′ " with microscope-slip 1 mm. in thickness (t = 6.5mm.) = + 49′ " with two microscope-slips, 2mm. and 1.6 mm. in thickness (t = 3.9mm.) = + 36′ " by thoroughly mixed liquids in the tank) = - 3′ Thickness of liquid layer in tank = 7.5 mm. On the emission theory such deviation is unaccountable, if our incidence be normal. Hence we may regard this as an experimentum crucis for the wave theory. I have been unable to find any previous account of it. The experiments were made at Canterbury College in August, 1900.