84. The velocity of light in vacuo is 3004 × 105 kilometres per second approximately. The periods of vibration of a sodium particle are about 1.9624 × 10−15 sec. and 1.9604 x 10-15 sec. Find the wave lengths of the two lights corresponding to the Frauenhofer double line D. [Let X be the wave length. Then 85. Explain the cause of the "aberration of light.” How does it affect the apparent Find its greatest value if the 184000 miles and that of the second. [Greatest value of aberration position of a star? velocity of light be earth 19 miles per 86. Prove that the convergeficence of a lens is equal to the refractive difference multiplied into the sum of the curvatures of the faces of the lens. [That is, with the usual notation show that 87. Find the convergeficence of a flint glass lens in water, the curvatures of the faces being equal to and. For flint glass μ=16, for water μ=1·336. [The index of refraction from water to flint glass is thus 1613361.1976. Hence the convergeficence=(1976)({+}) S8. What is the divergeficence of a double concave lens, the radii of curvature of its surfaces being equal and each of them 14 inches. Index of refraction 16. [Divergeficence (16-1)+'s) 14 89. What is meant by parallax generally? Taking the mean equatorial parallax of the sun as 8" 67, and the earth's mean equatorial radius as 3963-4 miles, calculate the sun's mean distance and express the parallax in radian measure. [There are 206,265 seconds in a radian. Again, let x=mean distance of the sun. 90. A plano-convex lens is used with its convex surface laid on a glass plate to show Newton's rings. The radius of the convex surface is 20 inches, and the rings are formed by light incident nearly normal to the glass plate. Find the radius of the second circle of maximum brightness for light of wave length 5.895 x 10-5 cm. [The general formula which gives the circles of brightness is where R=radius of nth ring, r-radius of curvature of lens, pangle of emergence of lens into the air, R=√320 × 2·54 × 5·895 × 10 −5 ='06672 cm. See Glazebrook, Physical Optics, page 138.] 91. A convex lens of crown glass of focal length 20 inches for B light is rendered achromatic for B and F rays by a concave lens of flint glass. Find what must be the focal length of the latter for B rays. What will be the focal length of the compound lens for B and F? Let f be the focal length for B rays of concave lens. 92. Describe experiments to show elementary phenomena of magnetic attraction and repulsion, and of magnetic induction. Explain the use of the armature applied to a piece of loadstone so as to enhance its power of supporting weights of soft iron. 93. Define the following terms:-Magnetic Dip; Declination; Isoclinic; Isogonic and Isodynamic lines. 94. A magnet moving in a horizontal plane like a compass needle is turned from its position of equilibrium through 15°, the magnet being 12 cms. long, and the force acting on each end being 5× 154 dynes. Find the moment of the return couple. [The arm of the couple Moment of couple 12 sin 15°=3·1056 cms.; 95. A bar magnet 8 centimetres long and weighing +grammes makes 11 oscillations per minute under the earth's horizontal force at Glasgow. Find the magnetic moment. The earth's horizontal force at Glasgow is 1522 in C.G.S. units. Let I=moment of inertia of the vibrating magnet; m magnetic moment of the magnet; and H-horizontal component of the earth's magnetism. 96. Describe the plate electrical machine, and explain carefully the electrical action of its various parts. 97. Describe the Leyden jar, and show how it is that the capacity of the jar is so much greater than it would be if the inside coating were removed from the jar and suspended in the air by a silk fibre. 98. Describe the construction and the electrical action of Volta's condensing electroscope, and show how to use it to test a feebly electrified body. 99. What is meant by the power of points? Describe experiments illustrating it. 100. Two small electrified pith balls are hung by a fine silk fibre from a fixed point and are kept apart by their mutual repulsion. The mass of each ball is gramme and the length of each fibre 120 cms. Taking as unit quantity of electricity the quantity |