converged to a single point, at the distance of half the radius of the mirror's concavity from the reflecting surface; but in separate points, at a little greater distance from the mirror than half the radius. Charles. Can you explain this by a figure? Tutor. I will endeavour to do so. Let AB (Plate II. Fig. 17.) be, a concave mirror, and M E any remote object, from every part of which rays will proceed to every point of the mirror; that is, from the point м rays will flow to every point of the mirror, and so they will from E, and from every point between these extremities. Let us see where the rays that proceed from м to A, C, and B will be reflected, or, in other words, where the image of the point м will be formed. James. Will all the rays that proceed from м, to different parts of the glass, be reflected to a single point? Tutor. Yes, they will, and the difficulty is to find that point: I will take only three rays to prevent confusion, viz. m a, M C, M B ; and c is the centre of concavity of the glass. Charles. Then if I draw c A, that line will be perpendicular to the glass at the point a : the angle M A C is now given, and it is the angle of incidence. James. And you must make another equal to it as you did before. Tutor. Very well: make c A x equal to MAC, and extend the line a x to any length you please. Now you have an angle м C C made with the ray м c, and the perpendicular c c, which is another angle of incidence.. Charles. I will make the angle of reflection c c z equal to it, and the line c z being produced, cuts the line a x in a particular point, which I will call m. Tutor. Draw now the perpendicular C B, and you have with it, and the ray м B, the angle of incidence м BC: make another angle equal to it, as its angle of reflection. James. There it is C B u, and I find the line B u meets the other lines at the point m. Tutor. Then m is the point in which all the reflected rays of м will converge; of course the image of the extremity M of the arrow E M will be formed at m. Now the same might be shown of every other part of the object M E, the image of which will be represented by e m, which you see is at a greater distance from the glass than half cc, or radius. Charles. The image is inverted also, and less than the object. CONVERSATION XII Of Concave Mirrors, and Experiments on them, TUTOR. If you understand what we conversed on yesterday, and what you have yourselves done, you will easily see how the image is formed by the large concave mirror of the reflecting telescope, when we come to examine the construction of that instrument. In a concave mirror the image is less than the object, when the object is more remote from the mirror than c, the centre of corcavity, and in that case the imn the object and mirror. age is Jame Suppose the object be placed in the centre c? Tutor. Then the image and object will coincide and if the object is placed nearer to the glass than the centre c, then the image will be more remote, and bigger than the object. Charles. I should like to see this illustrated by an experiment. Tutor. Well, here is a large concave mirror place yourself before it, beyond the centre of the concavity; and with a little care in adjusting your position, you will see an inverted image of yourself in the air between you and the mirror, and of a less size than you are. When you see the image, extend your hand gently towards the. glass, and the hand of the image will advance to meet it till they both meet in the centre of the glass's concarity. If you carry your hand still farther, the hand of the image will pass by it, and come between it and the body: now move your hand to either side, and the image of it will move towards the other. James. Is there any rule for finding the |