OPTICS. 
■ceded, thaj the case must be very different 
with those mirrors, the surfaces of which are 
spherical, whether convex or concave. Of 
the former it has been shewn that their pro- 
perty is to scatter and disperse the rays of 
light, to render those divergent which were 
parallel, to diminish the convergence of con- 
verging rays, and to augment the divergence 
of those which diverged before. The first 
obvious effect of these mirrors, therefore, 
must be to exhibit the image of the object 
which is opposed to them smaller than it is 
in reality. For the angle under which the 
rays strike the eye of the observer, must ne- 
cessarily be smaller in proportion to the con- 
vexity of the mirror. Suppose, for instance, 
■the object Cl) (fig. 13 .) placed before the 
convex mirror ab\ the two rays Cc and D cl, 
which proceed from the extremities of the 
object, and which, without the interposition 
of the mirror, would converge at /, are re- 
flected less convergent, and unite at /, form- 
jog an angle much more acute than they 
•would otherwise have done. The conse- 
quence, therefore, of the visual angle being 
so much more acute, is, that the image gh is 
proportioiiably smaller than the object it- 
self. 
The second effect of this dispersion of the 
rays is, that the image appears at a less dis- 
tance behind the glass than it would have 
done in a plane mirror. To understand this 
effect, it is necessary again to advert to a 
principle of optics which lias been just stated, 
viz. that objects are rendered visible not by a ! 
single ray of light proceeding from every 1 
point of the object, but that from every mi- 
nute point of the surface of every visible ob- 
ject pencils of divergent rays proceed, which 
are again converged on the retina of the spec- 
tator’s eye. 
Suppose then G (fig. 14 ) a luminous point 
of any visible object, from which a pencil of 
divergent rays proceed, and fall upon the 
convex mirror ab : these rays, agreeably to 
the nature of these mirrors, are reflected more 
divergent, and have their fictitious point of 
re-union (or virtual focus) g much nearer to 
the eye and to the surface of the mirror, than 
they would otherwise have. The image, 
therefore, as may be seen in the figure, in- 
stead of being at a distance behind the mirror 
equal to the distance at which the object 
stands before it (as would be the case in a 
plane mirror), will appear at a smaller dis- 
tance, and this distance will always be dimi- 
nished in proportion to the convexity of the 
mirror. 
For. the same reasons an object of a certain 
size, placed either perpendicularly or oblique- 
ly before a convex mirror, will necessarily 
appear curved or bent, because the different 
points of the object are not at equal distances 
from the surface of the mirror. All these 
effects will be very apparent from inspecting 
one of those small glass globes, lined with the 
common amalgam for making looking-glasses, 
which are sometimes suspended in old-lashion- 
ed apartments. In these the company seated 
in the room or round the table, are repre- 
sented by very minute images, which appear 
not at a certain distance behind as in plane 
looking-glasses, but very near the surface of 
the mirror, and always in some degree curved 
or distorted. 
The effects and phenomena of concave 
said, be the direct contrary to tlp>se of the point of that object ; it therefore ceases to be 
convex kind. The surface of. .concave inir- visible it these rays are converged to a point, 
furs is generally spherical (or in in the form and this happens when the object is not 
of a globe) ; though that is not always the 1 nearer to the minor than the principal ..topis, 
most convenient form for optical purposes, j To render, therefore, an object thus situated 
but it is that which is least difficult to the j visible, it is necessary that the eye should re- 
work men. 
The general effect of concave mirrors is, 
we have already seen, to render the rays 
more convergent. The point in which the 
converged rays unite is called the focus of 
converging rays; but this focus cannot be 
the same for all the rays incident on a con- 
cave surface. The parallel rays ab, de (tig. 
15 .), are converged by the mirror at the point 
F, which is distant from the mirror one-fourth 
j p :rt of the diameter of that circle, of which 
the mirror is a part or section ; and this is the 
point which is called the focus of parallel 
rays, and it is the real or principal focus of 
the mirror. The converging rays fg, hi, are 
cede so far beyond t he place ol the image h, 
as to allow the rays to cross each other, and 
meet the e\ e in a state of divergence. 
The image is in this cose always inverted. 
Such is the image ba of the object AB (tig. 
18 .). From this property of. the concave re- 
flector to form tlie image of an object, in 
these cases, before the reflector, many de- 
ceptions have been produced, to the great 
surprise of the ignorant spectator, hie is 
made to see a bottle half-full of water invest- 
ed in the air without losing a drop ot its con- 
tents; as he advances into a room, lie is 
tempted to exclaim with Macbeth, “ is this 
a dagger that 1 see before me > ’ and when he 
reflected upon the same principles more con- j attempts to grasp it, it vanishes into the atr. 
vefgent, and unite at the point K, nearer to i A variety of similar appearances may be 
the surface of the mirror than the principal ! represented, which are all produced by means 
focus. In fine, the divergent rays Ilwi and of a concave mirror, having an object he- 
lm, which proceed from the point R, beyond fore it strongly illuminated, care being taken 
the principal focus, unite at the point P. But that only the rays of light reflected from 
if the point of divergence was nearer the the object shall fail upon the concave refiect- 
mirror than the principal focus, as for in- or, placed in such a manner that the image 
stance at K, they would still be reflected di- shall be in the middle of the adjoining room ; 
ergent, and would proceed one towards /. or, if in the same room with the object and 
and the other towards h. j reflector, a screen must be placed so as to 
Plane and convex mirrors exhibit, as has prevent the spectator from discovering them, 
been already mentioned, the image behind j A hole is then made in the partition between 
the giass or mirror, and in a situation con- ! the two rooms, or in the screen, through 
formable to that of the object; but concave ! which the rays pass by which the image is 
mirrors shew the image behind when the ob- j formed. 1 he spectator then, when he casts 
ject is placed between the principal focus and j his eyes upon the partition of the screen, 
the mirror, and then the image is larger than ' will, in certain situations, receive the rays 
the object. Let AB (fig. 16.) be the object j coming through" this small aperture. He will 
placed before the concave mirror EF, and ; see the image formed in the air ; he will have 
nearer to the mirror than its principal focus. ; no idea, it not previously acquainted with op- 
The two pencils of rays Ac, Bf, which pro- tics, of the nature of the deception ; and may 
ceed from the extremities of the object, and | either be amused, according to the inclina- 
which, without the interposition of the mir- tion of his friends, with tempting fruit, or be 
ror, would converge at a, are reflected more j terrified at the sight of a ghastly apparition, 
converging, and unite at D ; and making an I Since it is the property of a concave mirror 
angle greater or more obtuse than they would to cause those rays which proceed in a paral- 
otherwise have done, the image ab is conse- ! fol direction to its surface, to converge to a 
quentiy greater than the object. j focus ; and since the solar rays, from the hn- 
This image too appears at a greater dis- I mense distance of that body, may be consi- 
tance behind the mirror than the object is at j dered as parallel ; concave mirrors prove very 
before it. The reason of this will appear, if j useful burning-glasses : and the focus of paral- 
we suppose A (fig. 17 .) a point of any object I lei rays, or principal focus, is their focus or 
placed nearer to the mirror than the princi- ' burning-point. 
pal focus F, whence a pencil of divergent rays Cylindrical mirrors, such as that represent- 
proceed, and falling on the mirror, are (ac- j e d j n fjg. 19. are employed more for the pur- 
cording to the principles before laid down) i p 0Se of amusement than of philosophy. They 
reflected less divergent, and consequently ; are called mixed mirrors, because they pro- 
have their virtual or imaginary focus at a ; <j uce at the same instant the effects ot plain 
greater distance, than if the object had been j and of convex mirrors. Suppose, for instance, 
placed before a plane mirror. ! GF (fig. 20.) to be the Height of such a mir- 
If, on the contrary, the object is placed j ror, and AE an object placed before or rather 
farther from the mirror than tlie principal fo- j below it; all the rays which proceed from 
cus, as for instance at e, the rays cb, ed, being J the points A, B, C, I), E, tailing on the sur- 
only moderately divergent when they come j face GF of the mirror, and reflected to the 
in contact with the mirror, are reflected con- i eye at O, will represent the images of these 
vergent, and will represent at E an image of | different points at a, b, c, d, c, as they would 
the object. If the eye, therefore, is with- be represented in a plane mirror; and with 
drawn to a sufficient distance (to 0 for ex- 
ample) for the rays to cross each other, it 
will perceive the image suspended in tlie air 
at E between the mirror and itself. The rea- 
son of this depends upon what has been already 
stated. Every object is rendered visible to 
mirrors will obviously, from what has been j us by pencils of divergent rays from every 
I P p 2 
respect to these, the dimensions of the object 
will not be altered in the corresponding image. 
But since the mirror is also curved, if we sup- 
pose the space q, t, y, (fig. 21.) to represent 
a part of its circumference, the rays Aq, L?-, 
M.q N t, Ot, IT, F y, being reflected to the 
eye at Z, will exhibit all these points A, L, 
