158 Mr. A. A. Common [May 30, 



substance of the lens and the curvature we give to the surfaces, and 

 not at all upon the aj)erture or width of the lens. The brightness 

 only of the picture of the star, depends upon the size of the lens, as 

 that determines the amount of light it gathers together. If, instead of 

 one star we have three or four stars together, we will find that this 

 lens will deal with the light from each star just as it did with the light 

 of the first one, and just in proportion to the angular distance they 

 are apart in the sky, so will the pictures we see of them be apart on 

 our screen. So if we let the light from the moon fall on our lens, all 

 the light from the various parts of the moon's surface will act like 

 the separate stars, and produce a picture of the whole moon (in the 

 photographic camera the lens produces in this manner a picture of 

 objects in front of it, and this picture we see on the ground glass). 

 When we attempt to get pictures of near objects that do not send 

 rays of light that are parallel, we find that as the rays of light from 

 them do not fall on the lens at the same angle to the axis, the 

 picture is formed further away from the lens. The nearer the object 

 whose picture we wish to throw upon the screen is to the lens, the 

 further the screen must be moved. If we try this experiment we 

 shall find, when we have the object at the same distance as the screen, 

 the picture is then of the same size as the object, and the distance 

 of the screen from the lens is twice that which we have found as 

 the focal length ; on bringing the object still nearer the lens, we 

 find we must move the screen further and further away, until when 

 the object is at the focus the picture is formed at an infinite distance 

 away, or, what is more to our purpose, the rays of light from an 

 object at the focus of a convex lens after passing through the lens 

 are parallel, exactly as we have seen such parallel rays falling on the 

 glass come to a focus, so that our diagram answers equally well 

 whatever the direction of the rays ; and this holds good in other 

 cases where we take the efiect of reflection as well as refraction. 



We can also produce pictures by means of bright concave surfaces 

 acting by reflection on the light falling upon them. Such a mirror 

 or concave reflecting surface as I have here will behave exactly as 

 the lens, excepting, of course, that it will form the picture in front 

 instead of behind. The bending of the rays in the case of the convex 

 lens is convergent, or towards the axis, for all parallel rays; if we 

 use the reverse form of lens — that is, one thicker at the edge than in 

 the middle — we find the reverse efiect on the parallel rays ; they will 

 now be divergent, or bend away from the axis ; and so with reflecting 

 surfaces if we make the concavity of our mirror less and less, till it 

 ceases and we have a plane, we shall get no efiect on the parallel rays 

 of light except a change of direction after reflection. If we go beyond 

 this and make the surface convex we shall then have practically the 

 same efi'ect on the reflected rays as that given to the refracted ray by 

 the concave glass lens. 



As regards the size of the picture produced by lenses or mirrors 

 of difierent focal length, the picture is larger just as the focal length 



