Stage 3. You are not permitted to answer more than five questions. 1. Give a careful account of the theory of the "colours of thin plates." (60) 2. Describe any method of obtaining the refractivity of a gas. (60) 3. Explain the formation of spectra by the concave grating and give a short account of Rowland's method of mounting the grating. (60) 4. How has the rotation of the plane of polarised light been explained? What is the essential difference in the character of the rotation produced by a sugar solution and by water in a magnetic field? 5. Explain the formation of the primary rainbow. (60) (60) 6. Give an account of Michelson's modification of Foucault's revolving mirror method of measuring the velocity of light. (60) 7. Describe experiments by which the pressure of light has been directly observed and measured. (60) Honours. PAPER I. You are not permitted to answer more than five questions. Candidates who do well in Paper I. will be summoned to South Kensington or some other centre to undergo a further examination, which will consist of (1) another paper, and (2) a practical examination in the laboratory. NOTE.-No candidate will be credited with a success in this examination who has not obtained a previous success in Stage 3, or in Honours, of the same subject. 1. Give an account of the methods which have been used to observe the anomalous dispersion produced by sodium vapour, and describe the character of the observations. (40) 2. Give a short description of the Zeeman effect and of the theory which has been advanced to account for the phenomenon. In certain cases the observations do not agree with the simple theory: discuss these. (40) 3. Describe the phenomenon of phosphorescence. To what has its occurrence been attributed? (40) 4. Explain the occurrence of Talbot's bands, paying attention to the importance of the side from which the film is introduced. (40) 5. To what is the blue colour of the sky attributed? Consider the question in conjunction with the fact that wireless waves are poorly transmitted during daylight. (40) 6. Prove that the time of passage of light from a point P in one medium to a point Q in another is a minimum. (40) 7. Find an expression for the aberration of a ray parallel to the axis of a lens, incident at a distance x from its centre. How would you investigate the curvature of field of a lens? (40) PAPER II. You are not permitted to answer more than five questions, of which one must be from Section A. The time allowed for this examination is three hours. SECTION A. 1. Write an Essay on the theory of dispersion, 2. Write an Essay on the nature of white light. SECTION B. 3. Give the theory of the Echelon spectroscope. Explain its limitations, and the precautions required in construction and adjustment. 4. Discuss Fresnel's theory of the reflection of light from a metallic or crystallic surface, and describe a method of verifying the theory experimentally. 5. Compare and criticise experimental methods of measuring the index of refraction and dispersive power of gases. 6. Explain what is meant by the focal length of a system of lenses, and describe how you would measure it. 7. A circularly polarised wave is incident normally on a thin crystal plate : give an expression showing how the emergent wave depends on the thickness and optical properties of the crystal. PRACTICAL EXAMINATION. The time allowed for this examination is six hours. 1. Plot a curve showing the relation between the refractive index for sodium light and the strength of a solution of the given substance. 2. Determine the wave-length of light of the given colour by measuring the diffraction bands produced by the given body. 3. Plot a curve showing how the candle-power of the given electric lamp varies with the voltage applied to its terminals. 4. Determine the curvature of the surface of the given lens by measuring the diameter of Newton's rings. Stage 2, Stage 3, and Honours. You may take Stage 2, or Stage 3, or, if eligible, Honours, but you must confine yourself to one of them. The examination in this subject lasts for three hours. Stage 2. You are permitted to answer only seven questions. 1. Describe carefully how you would determine the true coefficient of expansion of a liquid, being given that of mercury. (28) 2. How would you determine the increase in volume which occurs when water solidifies? (28) 3. Describe and explain Joly's method of determining the specific heat of gases at constant volume. (28) 4. What is meant by the critical state of a gas? Explain how the critical temperature may be determined. (30) 5. Estimate the rate at which ice may be expected to form on a pond when it is 5 cm. thick and the temperature of the air is 12° C., if the conductivity of ice is 0.0022 C.G.S. (28) 6. Why is it that on the first frost of a winter shallow waters freeze sooner than deeper ones, while on a second freezing after a slight thaw, there is much less difference to be noted? (28) 7. A quantity of air saturated with aqueous vapour occupies a volume of 100 c.c at 15° C. under a pressure of 76 cm. of mercury. The pressure is increased to 150 cm. at constant temperature and the volume is thereby halved; find the pressure exerted by the vapour. (30) 8. What is meant by the mechanical equivalent of heat? Explain the assumptions necessary to calculate its value from the specific heats of air at constant pressure and volume. (28) 9. How would you measure the diathermancy of a gas? Describe the apparatus required, and give a general account of any results which have been obtained. Stage 3. You are not permitted to answer more than five questions. (28) 1. Explain how the coefficient of linear expansion of crystals has been determined, and describe the general character of the results obtained, (60) 2. Describe an experimental method suitable for determining the density of a saturated vapour. (60) 3. What are the conditions which determine whether a solid will pass directly into the state of vapour or first liquefy on heat being supplied it? (60) 4. How would you determine the coefficient for the variation of surface tension with temperature? From general considerations, what would you expect its sign to be? (60) 5. Give a short account of the method employed in determining underground temperatures, and of the character of the results obtained. How have they been utilized for calculating the conductivity of rock, &c.? (60) 6. Describe the experiments of Joule and Thomson on the flow of gas through a porous plug. What bearing has this experiment on the regenerative process of liquefying air? (60) 7. Give some account of the equation of Van der Waals and of the theory of corresponding states. (60) Honours. PAPER 1. You are not permitted to answer more than five questions. Candidates who do well in Paper I. will be summoned to South Kensington or some other centre to undergo a further examination which will consist of (1) another paper, and (2) a practical examination in the laboratory. NOTE. No candidate will be credited with a success in this examination who has not obtained a previous success in Stage 3, or in Honours, of the same subject. 1. Explain how the variation of the melting point with pressure is related to the change in volume accompanying liquefaction, and to the change of vapour-pressure with (40) 2. Give a short account of the work which has been done on the variation with temperature of the specific heat of water. pressure. (40) 3. What is meant by the inversion point of the Joule-Thomson effect in the irreversible expansion of gases? Assuming Van der Waals equation, find the inversion points. (40) 4. Show how the surface tension of a liquid is connected with the latent heat of vaporization. (40) 5. Discuss the theoretical basis for Stefan's law of radiation, and Wien's law of distribution of energy in the spectrum of radiation. (40) 6. Find a general expression for the difference of the specific heats at constant pressure and volume. Find the form of the characteristic equation of a substance obeying Boyle's law for which the difference of the specific heats is (40) 7. Find the condition of stability of a small air bubble in water, when the vapour-pressure in the bubble exceeds the pressure in the water close to the bubble. constant. (40) PAPER II. You are not permitted to answer more than five questions, of which one must be taken from Section A. The time allowed for this examination is three hours. SECTION A. 1. Write a critical Essay on the laws connecting radiation and temperature. 2. Write an Essay on the law of Corresponding States. SECTION B. 3. Discuss the relation between the viscosity and conductivity of a gas, and describe carefully one method by which either viscosity or conductivity may be measured. 4. Describe the principal phenomena of osmotic pressure, and show how it is related to the vapour-pressure and to the depression of the freezing-point. 5. Find a general expression for the cooling effect in expansion through a porous plug, and deduce the characteristic equation of a substance for which the cooling effect is zero. |