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University of New Zealand.

B.A. Examination for Honours, 1885.

Mathematics and Mathematical Physics.

Paper e (2). Light.

Examiner: Prof. Silvanus P. Thompson, D.Sc., B.A.

1. Let two media of different refrangibility be separated by a spherical surface. Let a pencil of rays emanate from a point in one medium, and let the distance of the focus of the incident pencil from the principal focus for the first medium be called d, and the distance of the focus of the refracted pencil from the principal focus for the second medium be called d', and let the principal focal lengths for the first and second media be called f and f' respectively; prove that

dd'=ff.'

2. When the flat bottom of a dish or other vessel is viewed through a parallel water-surface it appears deeper at the point immediately below the eye than at other points. Discuss and explain this.

3. Two media are separated by a plane surface. Show that to an eye situated in the more highly refringent medium at a distance a from the surface a solid can be presented which, as viewed through the surface, shall appear as a flat plane parallel to the surface at a distance b beyond it; and show further that this solid will be an ellipsoid of revolution lying within the critical cone of rays, the ellipsoid having as the values of its

semi-axes respectively; μ, being the relative index of refraction of the two media.

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4. What are the conditions of achromatism of a pair of prisms? Explain also how a pair of prisms may be combined so as to give dispersion without deviating the rays of mean refrangibility.

5. Give a brief enumeration of the chief points in the wave-theory of light. How do you account, on that theory, for the existence of dispersion?

6. Explain the existence of "fringes" outside the edge of the geometrical shadow of an opaque body placed in simple diverging light.

7. In all the experiments to produce interference between two lights, with Fresnel's mirrors, biprism, &c., we invariably employ two images of the same source of light and not two actually independent lights. Why is this? What knowledge have we as to continuity in the emission of light rays from a luminous body?

8. State the law connecting absorption of light and the thickness of the absorbing medium.

A crystal of Brazilian tourmaline cut to a sphere appears of a clear green in every direction at right angles to the optic axis, but is absolutely opaque as viewed along the optic axis. Remembering that tourmaline transmits the extraordinary ray and suppresses the ordinary one, what conclusion do you draw from this observation as to the direction of the vibrations of the ray with respect to the plane of polarization? Are they executed in the plane of polarization at right angles to it?

9. A beam of polarized light falls upon a substance whose refractive index is μ. Calculate the relative intensities of the reflected and refracted portions, (a) when the incident beam is polarized in the plane of incidence, (b) when it is polarized perpendicularly to the plane of incidence.