CHAPTER XIII.

REFLEXION AND REFRACTION

MIRRORS AND LENSES.

NEARLY all the methods used in optical measurements are indirect. The quantity required is deduced by calculation from the quantities actually measured, or the law to be demonstrated is inferred from the actual observations by a process of reasoning. This is illustrated by the following experiment on the law of reflexion and by the experiments on focal lengths. The law of refraction may also be verified by the measurements of the refractive index of a transparent medium.

47. Verification of the Law of Reflexion of Light.

In order to prove the law, that the angle which a reflected ray makes with the normal to a plane surface is equal to the angle made by the incident ray with the normal, and that the two rays are in the same plane with the normal, two methods may be adopted :

(1) The direct method, in which the angles of incidence and reflexion are measured and compared, and the positions of the rays determined.

(2) An indirect method, in which some result is verified which may be theoretically deduced on the assumption that the law holds.

The following experiment is an example of the second method.

It may be proved, by assuming the law of reflexion, that an image of a luminous point is formed by a plane mirror at a point on the normal to the plane surface drawn through the luminous point, and at a distance behind the mirror equal to the distance of the luminous point from the front of the mirror. This we can verify experimentally.

Take as the luminous point the intersection of cross-wires mounted on a ring, which can be placed in any position in a clip.

We can place another similar cross in the exact position occupied by the image in the mirror of the first, in the following manner.

Scrape a horizontal strip of the silvering off the back of the mirror and place the one cross in front, so that on setting the eye on a level with the cross, half of the image is seen coming just to the edge of the silvering.

Then place the other cross behind, so that it can be seen through that part of the glass from which the silvering has been scraped. Place this second cross so that the upper half of it can be seen through the gap, and so that the intersection of the second appears to coincide with the image of the intersection of the first. In order to determine whether or not this is really the case, move your eye from side to side across the first cross-wire, then if the second cross and the image are coincident, the two will appear to move together as the eye moves, and will remain coincident wherever the eye is placed. If, however, the actual cross is nearer to the mirror than the image, then on moving the eye to the right the two will appear to separate, the further, viz. the image, going to the right hand, the real cross to the left.

Place, then, the second cross so that on moving the eye from side to side no separation between the cross and the image occurs. It is then in exactly the same position as that occupied by the image of the first cross in the mirror.

Let the first cross be placed at a distance of 1 foot (about) from the reflecting surface of the mirror. Measure the distance by means of a pair of compasses and a scale, and measure, also, the distance between the same surface of the mirror and the second cross, which has been accurately placed to coincide with the image of the first in the mirror. Then displace the second cross from coincidence with the image and replace it and read the distance again in order

to ascertain the limit of accuracy to which your observation can be carried. Repeat three times.

The experiment may be very conveniently made with a piece of unsilvered plate glass instead of the mirror. The image of the first cross formed by reflexion at the surface of the glass is generally sufficiently bright to permit of the second cross being accurately placed to coincide with it. If the glass is very thick, allowance must be made for the displacement of the image of the second cross as seen through the glass. A corresponding allowance may, of course, also be necessary in the case of the mirror whose thickness will alter the apparent position of the reflected image of the first

cross.

Two vertical pins in stands may be used instead of cross-wires, and the upper part of the second one may be viewed directly over the top of the mirror, while the lower part of the image of the first is seen in the mirror.

In order to verify that the image and object are on the same normal to the mirror, place the eye so that the image and object are in the same straight line with it, and notice that the image of the eye is in the same line too, no matter how far from or how near to the mirror the eye be placed; this can only be the case if the line is a normal.

In case the result obtained does not apparently confirm the law of reflexion, the discrepancy may be due to the fact that the mirror is cylindrical or spherical and not truly plane. To distinguish between the cases, repeat the experiment, moving the eye vertically up and down instead of horizontally.

Experiment.- Verify the truth of the law of reflexion of

The following method of finding the angle of a prism is another illustration of the law of reflexion :—

Place the prism on a sheet of paper attached to a drawing-board. Let BAC (fig. 23a) be its trace, A being the angle to be measured.

P

Stick a pin (P) vertically into the board at some distance from A, in such a position that images by reflexion can be obtained from the faces A B and A C respectively. Determine the positions of these images as for a plane mirror, or proceed as follows:-Look at one image, moving your eye about until it is seen as nearly as possible in a line with A; and place pins at Q, R, So that

the image of B
P, the edge A,
and the pin at
Q appear in
one straight
line, while the
image, the

R

FIG. 234.

edge, and the pin at R are seen in another. Then a ray PA falling on one face very close to A is reflected along A Q, while an almost coincident ray incident on the other face is reflected along A R. Join a P, A Q, A R, and measure with a protractor the angles QAR and BA C. It will be found that Q AR = 2 BAC; that is, that the angle between the reflected rays is twice the angle of the prism. This can be proved to be a consequence of the law of reflexion.

Experiment. Determine the positions of the images of a pin formed by the light reflected from the two surfaces of a prism, and thence measure the angle of the prism.

Y

48. The Sextant.

The sextant consists of a graduated circular arc, B C (fig. 24), of about 60°, connected by two metal arms, A B,

A plane mirror, M, is attached to this arm and moves with it. The plane of the mirror passes through the centre of the circular arc and is at right angles to the plane of the scale.

The mirror is known as the index glass, and is held by adjustable screws in a frame which is rigidly connected to the arm A D. By means of the screws it can be placed so that its plane is accurately perpendicular to that of the arc.

At F on the arm A C is another mirror called the horizon glass, also secured by adjustable screws to the arm. Its plane should be perpendicular to that of the arc and parallel to that of the movable mirror м when the index at D stands at the zero of the scale.

The upper half of the mirror F is left unsilvered. At G on the arm A B is a small telescope, directed towards the mirror F. The axis of the telescope is parallel to the plane of the arc, and by means of a screw at the