Experiments.

(1) Test the accuracy of the various adjustments of the sex

tant.

(2) Measure the angular distance between two distant points.

(3) Measure the altitude of a distant point, using an artificial horizon.

True angular distance 32° 32′ 55′′

Similarly for observations of altitude.

O. Refraction of Light through a Plate and through a Prism.

The path of a pencil of light through a plate or a prism may be traced and the law of refraction verified by a graphical construction in the following manner.

Place a rectangular block of glass, which should be of considerable size-say 8 or 10 cm. square by 1 cm. highon a sheet of paper fastened to a drawing-board, and mark its position A B C D (fig. xxv) on the paper. Draw a line P Q meeting the glass obliquely, and stick two pins vertically into the board at two points some distance apart in P Q.

On looking obliquely through the opposite face (C D) of the glass the two pins will be seen, and it will be usually possible to place the eye in such a position that the one may appear exactly behind the other. Do this, and stick two more pins into the board in front of the glass in such a way that these two are seen in the same straight line as the first two, so that all four appear to be in line one behind the other. Draw with a ruler a line R S through

the feet of the last two, and let it meet the surface of the glass in R. Join QR. Then a ray of light falling on the glass in the direction P Q is refracted into the glass along QR, and

on emergence travels along R S. On completing the figure it will be seen that PQ is parallel to R S. Draw M QN normal to the glass at Q. Then MQP is the angle of incidence 9, and NQR the angle of refraction

'.

To Verify the Law of Refraction (viz. that sin /sin o' is constant) and find the Refractive Index.

With Q as centre and QR as radius describe a circle cutting Q P in P. Draw PM perpendicular to the normal Measure the distances P M and R N, and take the

Q M.

Take a second incident ray P, Q, incident at a different angle, and determine the refracted ray R, S, in the same way. Then we shall have

PM

and it will be found that the ratios and PI MI

R N

are equal. RI NI

Thus this ratio is a constant for all angles of incidence, and the value of this constant is the refractive index. We have thus verified the law of refraction and found με the index of refraction.

To Illustrate the formation of a Caustic Curve by

Refraction.

Stick a vertical pin into the board in contact with the block at o. Let oN be a normal meeting the opposite

face in N, and along that face mark off a number of points P1, P2, Pg.. such that N P1 = P1 P2 = P2 P3 =. . .=1 cm.

suppose.

...

...

At each of the points N, F1, P2, . . place pins in contact with the block. Look at the block from a little distance, and place another series of pins in the board successively in such positions that the pin o, each of the pins N, P1, P2, . . in turn, and the corresponding pins, M, Q1, Q2, . . . of this next series appear successively in straight lines. Remove the block, join Q, P1, Q2 P2, Q3 P3, . . ., and produce each of these lines backwards to the point in which it meets the next preceding line. Let these points be R1, R2, R3. Then a ray travelling in the block along O P2 is refracted so as to emerge along P2 Q2, and so for the other rays.

Again, if we can suppose two consecutive emergent rays P2 Q2, P3 Q3, to reach the eye, these rays will appear to diverge from R2, and the position of the image of o which the eye sees when looking along Q2 P2 will be R2. In reality, the rays P2 Q2, P3 Q3 are too far apart to be treated as consecutive rays; we should have to suppose incident rays to fall on all the points of the glass between N and P, and draw all the emergent rays. In this way we should obtain a series of points, such as R1, . . . R。, all lying on a curve, each point being the intersection of two consecutive emergent rays. This curve is called the caustic curve, and to it all the emergent rays are tangents, while the virtual image of o seen in the direction of any given ray is the point in which that ray touches the caustic curve.

If, then, the figure be constructed as already described, and a curve drawn to touch all the emergent rays, this curve will be the caustic. The same figure can be used to verify by a geometrical construction the law of refraction.

To find the Refractive Index.

The following is another method of finding μ :

Make a mark at a point a (fig. xxvii) on one face of the block. This may be done by sticking on to it a small piece of sealing-wax. Place the block on the table, and stick a pin upright into the board in such a way that A1,

the head of the pin, is at the same height as A.

On look

ing through the block the reflected image of the pin and

until these two, when viewed directly from a point behind the pin, appear to coincide.

In this case A B A1, cutting the block in B, will be normal to the block, and if A' is the refracted image of A, it is also the reflected image of A1.

Since the light is nearly directly incident, we know that
BAμBA';

and since a' is the reflected image of A1,

Hence to find, measure the thickness of the block and the distance BA, of the pin from the block. The ratio of the two is the refractive index.

To Verify the Law of Reflexion.

Similar experiments can be performed to verify the law of reflexion. In this case let PQ (fig. xxviii) be an incident