TRINITY COLLEGE.

Mr. Stephenson's Paper.

OPTICS.

1. Given the distance of the focus of incident rays from the centre of a given spherical reflector, find the distance of the geometrical focus of reflected rays from the centre, when they are incident nearly perpendicularly.

2. Given the position of an object placed between two plane reflectors inclined at a given angle; find the total number of images, and apply it to the case where the angle of inclination is equal to 11° 15′

3. A straight line is placed before a concave spherical reflector, at the distance of one third of its radius from the surface; find the dimensions of the curve formed by its image, radius of reflector being 9 inches

4. Having given the ratio of the sines of incidence and refraction, when a ray passes out of one medium into each of two others, to find the ratio of the sine of incidence to the sine of refraction out of one of the latter mediums into the other.

5. When parallel rays are incident nearly perpendicularly upon a spherical refracting surface the distance of the intersection of the refracted ray and the axis, from the centre, is the greatest when the arc is evanescent.

6. A pencil of parallel rays passes from water through a globule of air; find the focus after the second refraction.

7. Find the focal length of a compound lens.

8. Explain the construction of Newton's telescope, and shew how it must be adjusted to the eye of a long-sighted person.

9. An object whose real depth below the surface of the water is ten feet, is viewed by an eye

fifteen feet above the surface. What must be the focal length of a lens through which it is viewed, that its apparent depth may be ten feet?

10. If a plane mirror be turned round uniformly the angular velocity of the image of a given object formed by continual reflection at its surface: angular velocity of reflector :: 2 : 1

11. The radii of a spherical reflector and sphere of glass of same aperture and power are in the proportion of 3 1. Compare the density of rays in sun's image formed by them.

12. Two straight lines are inclined at a given angle and a point E is given without them, a line E F f moves round the point E, and cuts the given lines in F and f; find the locus of the mirror D, so that f shall always be the image of F.

13. Suppose a mirror M to move in a straight line AB, and an object D in the line AC at right angles to it, and distance between object

D

and mirror to be con- A

M B

stant; to determine the locus of an eye, which being always the same distance as the object from the mirror, shall always see the object.

14. Having given the refracting powers of two mediums, to find the ratio of the focal lengths of a convex and concave lens, formed of these substances, which, when united, produce images nearly free from colour.

15. When a ray of light is incident obliquely

upon a spherical reflector, to determine the intersection of the reflected ray and the axis of the pencil to which it belongs, and shew that when the focal length is given, the longitudinal aberration of parallel rays varies as (lin. apert.) and lateral aberration varies as (lin. apert.)3

16. If an object be placed in the principal focus of a double convex lens, the visual angle is the same, whatever be the distance of the eye from the glass.

17. Find the length of a caustic generally, and apply it to the case when the reflecting curve is a semicycloid, rays parallel to axis.

18. Find the density of rays in a caustic, when reflecting surface is a hemisphere, radiating point in surface.

TRINITY COLLEGE.

Mr. Sheepshanks' Paper.

HYDROSTATICS.

1. The pressure of a fluid against any surface in a direction perpendicular to it, varies as the area of the surface multiplied into the depth of its centre of gravity below the surface of the fluid.

2. A hollow cone without a bottom stands on a horizontal plane, and water is poured in at the vertex. The weight of the cone being given, how far may it be filled so as not to run out below? 3. What must be the magnitude and point of application of a single force that will support a sluice-gate in the shape of an inverted parabola?

4. Find the specific gravity of a body which is lighter than the fluid in which it is weighed.

5. If the specific gravity of air be called m, that of water being 1, and if W be the weight of any body in air, and W its weight in water, its weight in vacuo will be,

m

W+

(W—W').