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lengths fi and f, in contact. Prove that for any number of such lenses placed in contact 1/F=E(1/f).
78. What is the focal length of a lens which is equivalent to two thin convergent lenses of focal lengths 15 cm, and 30 cm. placed in contact ?
79. A concave lens of 8 cm. focal length is combined with a convex lens of 6 cm, focal length : what is the focal length of the combination ?
80. A convex lens of focal length 16 cm, was placed in contact with concave lens, and the focal length of the combination was found to be 48 cm. Calculate the focal length of the concave lens.
81. A candle is held i foot in front of a convex lens, and a distinct image of the flame is formed on a screen placed 4 inches behind it. A concave lens is now placed in contact with it, and it is found that the screen has to be moved 8 inches farther off in order to receive the image. What is the focal length of the concave lens ?
82. Explain the action of a condensing lens when used as a magnifying glass. Give a sketch showing how the image is produced, and prove that the magnifying power is approximately equal to All, where A is the distance of most distinct vision.
83. Describe the action of the eye, considered as an optical instrument, and explain the causes of abnormal vision. Will the magnifying effect of a given readinglens be greater when used by a long-sighted or a shortsighted person ?
84. A person whose distance of most distinct vision is 20 cm. uses a lens of 5 cm. focal length as a readingglass : at what distance from a book must he hold it ? Also what will be its magnifying power ?
85. A long-sighted person can only see distinctly objects which are at a distance of 48 cm. or more : by how much will he increase his range of distinct vision if he uses convex spectacles of 32 cm. focal length ?
86. A short-sighted man can read printed matter distinctly when it is held at 15 cm. from his eyes : find the focal length of the glasses which he must use if he wishes to read with ease a book at a distance of
87. A convex lens produces an image of a candlefla upon a screen whose distance from the candle is l; the lens is displaced through a distance d, when it is found that a distinct image is again produced upon the
Show that the focal length of the lens is (12 – d2)/41.
88. Prove that the size of the object in the last question is a geometrical mean between the sizes of the two images produced.
89, In an experiment made according to the method of Ex. 82, the distance between the candle and screen was 255 cm. and the lens had to be shifted through a distance of 73.7 cm. What was its focal length ?
90. Calculate the mean value of the focal length of a convex lens which gave the following results by the method of displacement : Exp. 1
I=85 cm. d=38.7 cm.
d=33.0 » d=14.5 »
EXAMINATION QUESTIONS. 91. Describe a method of measuring the velocity of light (a) in air, (6) in glass, its velocity in air being known. In using Foucault's method it was observed that when the mirror was turning 257 times per second the displacement of the image was •113 metre, the distance between the slit and the moving mirror being 8.58 metres, and between the two mirrors 605 metres. Show that the velocity of light is 296,000,000 metres per second.
Camb. Schol. 1883. 92. State the principles on which the illuminating powers of two sources of light are compared. The distance between two incandescent lamps, of 16 and 25 candle-power respectively, is 6 feet. Show that there are two positions, on the line joining the lamps, in which a screen may be placed so as to receive equal illumination from each lamp, and determine these positions.
Prel. Sc. 1887. 93. On a moonlight night, when the surface of the sea is covered with small ripples, instead of an image of the moon being seen in the sea, a long band of light is observed on the surface of the sea extending towards the point which is vertically beneath the moon. Account for this phenomenon in accordance with the laws of reflection, illustrating your explanation by a figure.
Matric. 1882. 94. What is the index of refraction of a transparent substance ?
A plate of glass 6 inches thick with a refractive index of 1.5 is placed 2 inches above a luminous object. Make a careful full-sized drawing showing the path of a small conical pencil of light through the plate, the axis of the pencil being normal (or perpendicular) to the surface of the glass, and show where the image of the object will appear to an eye placed on the other side of the plate.
Matric. 1884. 95. Define the term "the refractive index of a transparent medium,” and give an account of experiments by which that of a liquid may be measured.
The refractive index of water is 1.33, and the velocity of light in air is 300,000,000 metres per second. Find its value in water, stating the experimental grounds there are for your answer.
Ind. C. S. 1885. 96. Under what circumstances is total internal reflection possible? A ray of light passing through a certain medium meets the surface, separating the medium front air at an angle of 45°, and is just not refracted. What is the refractive index of the medium ?
97. What is meant by saying that the refractive indices of glass and of water are 1.5 and 1.33 respectively? Show for which of these substances the critical angle, or limiting angle of refraction, is the greater.
Matric. 1885. 98. An image of a candle-flame eight times as broad as the flame itself is to be thrown, by means of a convex lens, on a wall at a distance of 12 feet from the candle. What will be the focal length of the lens required, and where must it be placed ?
Matric. 1885. 99. How is the focal length of a convex lens best determined without the aid of sunlight ?
An object is placed 8 inches from the centre of a convex lens, and its image is found 24 inches from the centre on the other side of the lens. If the object were placed 4 inches from the centre of the lens where would the image be ?
Matric. 1886. 100. An object 3 inches in height is placed at a distance of 6 feet from a lens, and a real image is formed at a distance of 3 feet from the lens. The object is then placed i foot from the lens. Where, and of what height, will the image be ?
Matric. 1887. 101. A goldfish globe of 6 inches radius is filled with water. Determine the apparent position of a point inside the globe, 4 inches from its surface, when seen by an eye outside looking along a radius of the globe.
Int. Sc. 1884. 102. A small direct pencil of rays from a luminous point enters a refracting medium bounded by a spherical surface. Determine the image of the point.
Given a double concave lens of 5 cm. thickness, the radii of curvature of its faces being 15 and 20 cm. respectively. Find the position of the image of a point in the axis 24 cm. from the nearer face, aberration being neglected.
Int. Sc. Honours 1884. 103. Trace the position of the image of a bright point formed by a lens consisting of a sphere of glass,
of radius 2 inches and refractive index 1.5, when the point moves from an infinite distance up to the sphere.
Int. Sc. Honours 1885. 104. Explain fully how you would determine experimentally the index of refraction of a plano-convex lens for sodium light.
Int. Sc. Honours 1883. 105. A luminous point is placed in the axis of a glass hemisphere, for which j = 3/2, at a distance of a foot from the plane surface ; if the radius of the hemisphere be 9 inches, show that the rays after passing through it will be parallel.
Camb. Schol. 1886. 106. A small air-bubble in a sphere of glass 4 inches in diameter appears, when looked at so that the bubble and the centre of the sphere are in a line with the eye, to be i inch from the surface. What is its true distance ? (u= 1.5.)
Int. Sc. 1887. 107. A convex lens of 6 inches focal length is used to read the graduations of a scale, and is placed so as to magnify them three times; show how to find at what distance from the scale it is held, the eye being close up to the lens.
Owens Coll. 1886. 108. A pair of spectacles is made of two similar lenses, each having two convex surfaces of 10 and 20 inches radius respectively, and a refractive index 1.5. A person seeing through them finds that the nearest point to which he can focus is 1 foot away from the glasses. What is his nearest point of distinct vision ?
Camb. M.B. 1885. 109. How is a spectrum obtained by diffraction ? How does such a spectrum differ from a prismatic spectrum?
If a grating with 100 lines to the millimetre is placed in front of a slit illuminated with monochromatic light, and the angular distances of the ist and 2d images are found to be 2° 18' and 4° 35' from the central image, what is the wave length of the light?