17. Required the curve, in each point of which, the same given brightness, supposed equal to unity, will be produced by a given radiating point.

18. If (F) be the principal focal length of a triple object-glass, composed of three contiguous lenses, whose principal focal distances are P1, P2, P3, respectively; prove that

1. STATE the principal hypotheses which have been formed respecting the nature of light, and the objections which have been raised against each of them.

2. If light, diverging from a luminous point situated in a uniform transparent medium, lose an nth part of its rays in passing through any portion, its intensity after passing through equal successive intervals will decrease as the series

3. Having given the position of two lights of known intensities, to determine the nature and equation of the surface, of which every point shall be equally illuminated.

4. A reflector is formed by the revolution of a small arc of a catenary round its axis, and rays are incident on it parallel to each other, and to the axis: find the focus of reflected rays.

5. The reflecting curve is the reciprocal spiral, and the radiant point is situated in the pole: find the equation to the caustic.

6. The curvature of the image of a small portion of a sphere placed with its concavity turned towards a concave spherical reflector, is equal to the curvature of the object together with that of a sphere whose radius is the focal length of the reflector.

7. If be the angle of incidence of a homogeneal ray of light which passes through a prism, whose refracting angle is ; then

α

when the deviation (3) is a minimum, 0=+

8. If two parallel rays be incident on a transparent sphere, one perpendicularly, and the other at an angle of incidence = 0; the arc included between the emergent rays is one whose sine

9. If F be the focal length of a double convex lens, the radii of whose surfaces are r, r', and its thickness (which is small) = 1;

10. Determine the apparent magnitude of a straight rectilinear object, placed at a given depth parallel to a surface of water, the eye being situated in a given point in the plane which passes through the object perpendicular to the surface.

11. Find the form of a surface which shall refract parallel rays accurately to a point within it.

12. If 1 + r, 1 + v, be the ratio of refraction belonging to the red and violet rays respectively, in a lens whose aperture is D: the diameter of the least circle of aberration is

v-r

v + r

D.

13. Construct the Gregorian telescope; find its magnifying power, and greatest field of view.

14. Explain the Camera Lucida.

15. If m, n be the ratio of refraction belonging to the red and violet rays respectively in a double convex lens, with surfaces of equal radii r; and m', n' those in a double concave lens, and the two be placed so as to coincide; then if the radius of the exterior surface

the thickness of each being neglected.

16. If the rays of a small pencil of light fall upon a drop of water, and emerge parallel after p reflections within it,

TRINITY COLLEGE, 1825.

1. PROVE that a ray of light emanating from a given point, and reflected by a plane surface to an eye in a given position, describes the shortest path possible.

2. If rays nearly parallel be incident on a convex or concave spherical reflector, determine the relation between the distances, from the surface, of the foci of incident and reflected rays.

3. A ray of light emanating from a luminous point being incident at an angle tan.-'a, on a curve whose equation is

and thence deduce the general equation to a caustic by reflection.

4. When the reflecting curve is a O, and the radiating point on

ce

con

its O , prove that the caustic is a cardioide, whose base is a centric with the given O, and the radius of which is of the radius of the given O.

5. Find the least of aberration, into which a pencil of rays, reflected by a spherical surface, is collected.

6. Give Newton's demonstration of the fundamental law of refraction.

7. Explain the method of determining the refraction

(1). Of a transparent solid,

(2). Of a liquid,

(3). Of a gaseous body.

8. A small pencil of rays being incident on a spherical refracting surface bounding two different media, to find the focus of refracted

rays.

9. (1). If F represent the focal length of a double convex lens, the radii of whose surfaces are r and r′, and the sine of incidence be (m) times that of refraction, prove that

1

F

(2). How must this formula be modified, so as to exhibit

in the meniscus, and in the concavo-convex, and double concave lenses.

10. Prove that the conjugate foci move in the same or in opposite directions, according as the rays are incident on a refracting or a reflecting surface.

11. If a straight line be placed at right angles to the axis of a spherical reflector, or of a lens at a distance (a) from the centre, prove that the polar equation to the image is

in which r = distance from the centre of any point in the image.

♦ = angle subtended at the centre by the straight line,

f principal focal length of the reflector or lens ;

and thence determine the particular cases in which the image is an ellipse, hyperbola or parabola.

12. (1). Construct Newton's telescope, find its magnifying power, and determine its field of view.

(2). What advantage have reflecting telescopes over refractors?

13. If (F) be the focal length of a simple microscope, (c) the nearest distance of vision, then the greatest angle under which the image of a line (a) can be viewed is a

14. To find the centre and diameter of the least circle of chromatic aberration.

15. Construct an achromatic telescope.

16. Explain the manner in which the primary and secondary bows in the rainbow are formed, and find the altitude of the highest point above the horizon, and the breadth of the colours.

17. Describe the phenomenon of the coloured rings, which are formed by pressing together two plates of glass: and state and examine the hypotheses that have been advanced in explanation of this phenomenon.

TRINITY COLLEGE, 1826.

1. WHAT are the laws of Optics? How are they proved? 2. How does it appear that the propagation of light is gradual? 3. Find the equation between the focal distances for a spherical reflector. Shew that it answers equally for a convex as a concave

one.

4. Supposing that a mirror collects the Solar rays to a point at the distance of six inches, where will be the image of an object placed in front of it at twelve feet from its surface?

5. How may the radius of a convex reflector be found by an observation with the Solar rays?

of curvature through the luminous point.)

7. What is the caustic to a surface generated by the revolution of a cycloid about its axis?

8. What must be the length of a plane vertical mirror, in which a person may see his whole figure reflected ?

9. In what case is the image of a straight line produced by a spherical mirror an hyperbola?

10. What are the different species of lenses? Which of them are of the same nature?

11. Find the focal length of a lens, and shew that it is the same whichever side be presented to the incident rays.

12. What kind of glasses are used by persons who have been couched ?

13. How are the lenses made to achromatize each other?