QUEEN'S COLLEGE, 1828. 1. THE foci of incidence and refraction of rays falling nearly perpendicularly on a concave mirror of given radius, are on opposite sides of the mirror, and the focus of refraction twice as far from it as the focus of incidence; find their actual distances. 2. A pencil of parallel rays is incident nearly perpendicularly on a plano-concave lens of given thickness, and after reflexion at the plane side, which is silvered, is again refracted out of the lens; find the focus of emergent rays. 3. A sphere of air is included in a medium of glass through which parallel rays are passing. What portion of the rays incident on the sphere will pass through it? 4. Find the nature, length, and law of density of the caustic when the reflecting curve is a circular arc, and the focus of incident rays is in the circumference. 5. Given the radius of the arc of any colour in the primary rainbow: find the refraction when rays of that colour pass out of air into water. 6. At what altitude above the centre of a circular annulus must a luminous point be placed, that the quantity of light on the annulus may be the greatest possible? QUEEN'S COLLEGE, MAY 1829. 1. FIND the direction of a ray passing through a given point, so that after being reflected at two plane mirrors, given in position, it may pass through the same point again. 2. AC is vertical, CB horizontal, AB a straight line of given length, which reflects all rays incident upon it from a luminous point Q, placed at a given distance from C in CB produced. Find the inclination of AB that half the rays incident upon it may, after reflection, meet CA produced. 3. A luminous point is placed in the axis of a concave mirror of one foot radius, at the distance of three feet from it: to what point are the rays reflected? also, determine the ratio of the initial velocities of the foci of incidence and reflection in this case. 4. A luminous point is placed in the centre of gravity of a right cone, of a given altitude of a denser medium; and its vertical angle is as large as possible, that no rays incident on the base may be reflected. Required the content of the cone. 5. Find the nature, length, and variation of density, of the caustic, when the reflecting curve is a circle, and the focus of incidence is in the circumference. 6. Find the focal length of a double convex lens of equal radii and inconsiderable thickness: and then, supposing it to be double of either radius, determine the refractive power of the medium. Construct Newton's telescope; shew that objects appear inverted through it; find the field of view; and trace the course of a pencil of rays on supposition that a rectangular prism is substituted for the plane reflector. 8. A luminous point is in the middle of the axis of a hollow cylinder of given length, and just half the rays diverging from it fall on the interior surface. From these data, compare the intensity of the light at the edge, with that in the middle of the surface.. QUEEN'S COLLEGE, MAY 1830. 1. A LUMINOUS point is placed at a given distance in the perpendicular through the centre of a given square: find the whole light incident on the square. 2. A concave spherical reflecting surface is filled like a cup with water; given the focus of rays diverging from a point above the surface of the water, to find the focus of rays which emerge after having suffered two refractions and one reflection. 3. A luminous point Q, is placed at four feet distance, in the axis of a convex mirror of one foot radius; find the focus q of reflected rays: also find the ratio of their initial velocities, supposing Q to be put in motion. 4. A pencil of rays diverging from the centre of a sphere, after refraction at its surface, diverge from the opposite extremity of the diameter; required the refractive index. 5. A telescope consists of three convex lenses, whose focal lengths are as 30, 3, and 1; the latter two being at the distance 2 from each other: find the magnifying power, and trace the course of the rays. 6. On supposition of the Sun's light being homogeneous, shew what would be the nature and width of the primary rainbow; and determine from observations made on such a bow, the refrangibility of the light in passing out of air into water. 7. Prove that the deviation of a ray which passes through a prism in a plane perpendicular to its axis is a minimum when the incident and emergent rays make equal angles with the sides of the prism and shew that there could be no such minimum, if the angles of incidence and refraction, instead of their sines, were in a constant ratio. CORPUS CHRISTI COLLEGE, 1825. 1. WHAT are the two principal hypotheses which have been formed respecting the nature of Light? How has it been found that the action of light is not instantaneous? What are the three laws on which the theory of Optics is founded, and how are they established by experiment? 2. Q and q are the conjugate foci of a small pencil of parallel rays, incident nearly perpendicularly on a spherical reflector, F is the principal focus, QE=q, Eq=q', EF=ƒ; shew that 1 1 1 = + q f q and hence prove that Q and q lie on the same side of F, that they move in opposite directions, and meet at the centre and surface of the reflector. 3. Determine the aberration in reflection, at a spherical surface. 4. Parallel rays are incident on a parabola in a direction perpendicular to its axis; find the equation to the caustic by reflection, and the angle at which it cuts the axis of the parabola. 5. PR is a straight line placed before a spherical reflector, and inclined at a given angle to EP. Prove that its image is a conic section. Determine the angle which the axis-major makes with EP at E, and shew that the image is an arc of an ellipse, hyperbola, or parabola, according as EP cos o is greater than, less than, or equal to, one half the radius of the reflector. 6. Determine the deviation of a ray of light refracted through a triangular glass prism, and shew that it is a minimum, when the incident and emergent rays make equal angles with the sides of the prism. 7. If a plane reflector turn round an axis, shew that the angular motion of an image formed by reflection, is double that of the reflector. 8. A and A' are the distances of the foci of incident and refracted rays from the surface of a spherical refractor, whose radius =r, shew that the direction of incidence being nearly perpendicular to the surface, and deduce the values of A' for rays incident on the concave and convex surfaces, both of a rarer and a denser medium. 9. A Bab is a sphere whose radius=r, Bcb is a spherical surface whose radius = r', BAbc is glass, and Babc any other substance whose refracting power is given; if QA be a ray of light refracted through the sphere, find the geometrical focus of refracted rays. 10. Find the aberration in a lens whose thickness is inconsiderable. 11. If 1 + r, 1 + v, be the ratio of refraction for red and violet rays respectively, in a lens whose aperture =a, shew that the diameter of the least circle of chromatic aberration = 12. v-r v + r AB is a lens whose focal length a; suppose that a shortsighted person, unable to see distinctly objects beyond distance a, is a also unable to see those within the distance ; find the least value m of A, for which the above lens will be of use. 13. Construct the Gregorian telescope, and find its magnifying power. 14. Given the distance at which a short-sighted person can see distinctly, find the distance between a given object-glass, and a given eye-glass in the astronomical telescope, when adapted to such an eye, and to distant objects. 15. Determine the focus of a thin pencil of rays, after being refracted obliquely at a curve surface; and shew that if the surface be plane, vu:: sin. sin.p cos.24 cos.2p - where QP = u, Pq = v ; = angle of incidence, and p = angle of refraction. 16. The colours of the secondary rainbow occur in the inverse order of those in the primary. 17. Find the altitude of the highest point of the rainbow above the horizon, and the breadth of the colours. CORPUS CHRISTI COLLEGE, JUNE 1829. 1. EXPLAIN the properties of light upon which the laws of Optics depend. State how and by whom it was discovered that the propagation of light is not instantaneous, and describe accurately the experiment by which Newton determined that it was composed of rays differing in refrangibility and colour. 2. An object is placed between two plane mirrors not parallel. Find the number of images which will be formed of it by successive reflections, and apply the principle to explain the construction of the Kaleidoscope. 3. If a pencil of divergent rays be received upon any curved reflector at a distance u from its focus, the distance v of their inter section after reflection will be found from the equation 1 1 u ย c c being the chord of curvature passing through the focus of incident rays. 4. Determine the caustic by reflection at a spherical surface after two reflections of the incident rays, the luminous point being in any part of the surface. 5. Give a practical method of determining the refractive power |