# University of New Zealand. — Physical Science. — Paper b. Sound and Light

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## Paperb. Sound and Light.

1. Why does sound travel faster in water than in air? Describe some experiment proving this fact. Show how to calculate the theoretical velocity of sound in water from experiments made on the force required to compress it.

2. If a vibrating tuning-fork be held to the ear, and turned round slowly between the finger and thumb while so vibrating, it is noticed that there are four positions, nearly at right angles to one another, in which little or no sound is heard. Give a full explanation of this.

3. Explain the principle of the superposition of small motions. Show by a careful sketch the wave-form of the sound made by the simultaneous sounding of a note and its octave, and point out how this form will be modified by changing the phase of one of the components.

4. Show that for any ordinary thin magnifying lens there is, for every point that may be taken on the axis as a focus from which rays diverge, a conjugate point to which these rays will converge, and that that conjugate point will also be in the axis. Show that in a plano-convex lens having radius of curvature r, and index of refraction μ, the principal focal length f has the value

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5. Show that if in the usual formulæ for refraction at a single plane or spherical surface we substitute for the index of refraction the value—1, we obtain the corresponding formulæ for reflexion at a plane or spherical surface.

Does the quantity of light reflected at the surface of a substance depend in any way on its index of refraction?

6. Newton's rings are made by laying upon a plane sheet of glass a lens of small curvature. Suppose the radius of curvature of the surface to be two metres, and the wave-length in air of green light to be 0·00005 centimetre, calculate the diameter of the first bright ring as viewed by reflexion in green light at nearly normal incidence.

How would the system of rings be affected by running in bisulphide of carbon between the lens and the sheet of glass? How would the substitution of a polished silver plate for the sheet of glass then affect the rings?

7. Explain the system of prisms used in a direct-vision spectroscope. What is meant by irrationality of dispersion? How does it affect spectroscopic measurements of wave-lengths?

8. Describe and sketch the lens-system of an opera-glass. How must the positions of the lenses be altered to suit a shortsighted person?

9. The light reflected at the surface of a pond is partly polarized. How would you ascertain the position of the plane of polarization and the proportion of polarized rays present?