Encyclopaedia Britannica > Volume 15, NIC-PAR

Iieory.
OPT
lippear- 6. If in any of three last (cases, in each of
l Ce of Bo-which the image is lormed otr the same, side of the re-
TctionyfleCtlng SlU'filCe wIth the object, the eye he situated far-
iim differ-t,ier the surface than the ]>lace where the image
ntSur- ^lls, the rays of each pencil, crossing each other in
faces, the several points of the image, will enter the eye as
‘~y ' from a real object situated there ; so that the image
will appear pendulous in the air between the eye and
the reflecting surface, and in the position wherein it
is formed, viz;, inverted with respect to the object, in
the same manner that an image formed by refracted
light appears to an eye, placed beyond it; which was
fully explained under Prop. iv. and therefore needs not
be repeated.
But as what relates to the appearance of the object
when the eye is placed nearer to the surface than the
image, was not there fully inquired into, that point
shall now be more strictly examined under the follow¬
ing case, which equally relates to refracted and reflect¬
ed light.
7. If the eye he situated between the reflecting sur¬
face and the place of the image, the object is" then
seen beyond the surface ; and the farther the eye re¬
cedes from the surface towards the place of the image,
the more confused, larger, and nearer, the object ap-
1 >. 16.
pears.
To explain this, let AB represent the object; IM its
image, one of whose points AI is formed by the concur¬
rence of the reflected rays DM, EM, &c. which before
reflection came from B ; the other, I, by the concur¬
rence of DI, El, &c. which came from A ; and let
ai be the pupil of an eye, situated between the surface
DP and the image. This pupil will admit the rays
Hfl, KZ>; which, because they are tending towards I,
are such as came from A, and therefore the point A
will appear diffused over.the space RS. In like manner
the pupil will also receive into it the reflected rays K a
and L b, which, because they are tending towards M,
by supposition came from B ; and therefore the point
B will be seen spread as it were over the space TV, and
the object will seem to fill the space RV ; but the re¬
presentation of it will be confused, because the interme¬
diate points of the object being equally enlarged in ap¬
pearance, there will not be room for them between the
points S and T, but they will coincide in part one with
another : for instance^ the appearance of that point in
the object, whose representation falls upon c in the
image, will fill the space ?n n ; and so of the rest. Now,
if the same pupil be removed into the situation ef, the
reflected rays Ee and Gf will then enter the eye, and
therefore one extremity of the object will appear to co¬
ver the space XY ; and because the rays O f and L e
will also enter it in their progress towards M, the point
B, from w’hich they came, will appear to cover ZV ;
the object therefore will appear larger and more con¬
fused than before. When the eye recedes quite to the
image, it sees but one single point of the object, and
that appears diffused all over the reflecting surface : for
instance, if the eye recedes to the point M, then rays
flowing from the point B enter it upon •whatever part
of the surface they fall. The object also appears nearer
to the surface the farther the eye recedes from it to¬
wards the place of the image ; probably because, as the
appearance of the object becomes more and more con¬
fused, its place is not so easily distinguished from that
1 0 s, 239
of the reflecting surface itself, tilf at last when it is Apnear-
quite confused (as it is when the eye is arrived at M) ance of Bo-
they both appear as one, the surface assuming the colour^6 s seen by
of the object. Reflection
As to the precise apparent magnitude of an object
seen after this manner, it is such that the angle it ap- fates. *
pears under shall be equal to that which the image of v-^
the same object would appear under were we to sup- iSo*
pose it seen from the same place : that is, the apparent™"
object (tor such we must call it, to distinguish it from nitude of"
t ie image ot the same object) and the image subtend object
equal angles at the eye. seen by re-
Here we must suppose the pupil of the eye to be a iucUon
point only, because the magnitude of it causes a small ‘1°™ sue0"
alterat ion in the apparent magnitude of the object. Let face,
the point a represent the pupil, then will the extreme
j ay .-> that can enter it be H a and Jv a; the obieet there¬
fore will appear under the angle Ha K=Ma I, the
angle under which the image IM would appear were it
to be seen from a. Again, if the eye be placed in f, the
object appears under the angle G/0=I/M, which
the image subtends at the same place, and therefore the
apparent object and image of it subtend equal angles at
the eye.
Is ow if we suppose the pupil to have any sensible mag¬
nitude a b ; then the object seen by the eye in that situa¬
tion will appear under the angle HXL, which is larger
than the angle H a K, under which it appeared before ;
because the angle at X is nearer than the angle at a,
to the line IM, which is a subtense common to them
both.
From this proposition it follows; that, were the
eye close to the surface at K, the real and apparent
object would be seen under equal angles (for the real
object appears from that place under the same angle
that the image does, as will be shown at the end of
this section) ; therefore, when the eye is nearer to the
image than that point, the image will subtend a larger
angle at it than the object does ; and consequently,
since the image and apparent object subtend equal
angles at the eye, the apparent object must necessarily
be seen under a larger angle than the object itself,
wherever the eye be placed, between the surface and
the image.
As each point in the representation of an object made
by reflection is situated somewhere in a right line that
passes through its correspondent point in the object,
and is perpendicular to the reflecting surface; we may
hence deduce the following easy and expeditious method
of determining both the magnitude and situation of the *-
image in all cases whatever.
Though the extremities of the object AB and the Plate
centre C (fig. 17, 18, 19.) draw the lines AG BC, and cfCLXXxn‘
produce them as the case requires ^ these lines will be^ls" I^’ 1 *
perpendicular to the reflecting surface, and therefore 15
the extremities of the image will fall upon them.
Through F the middle point of the object and the
centre, draw the line EC, and produce it till it passes
through the reflecting surface; this will also be per¬
pendicular to the surface. Through G, the point where
this line cuts the surface, draw the lines AG and BG,
and produce them this way or that, till they cross the :
former perpendiculars ; and where they cross, there I
and M the extremities of the image will fall. For sup¬
posing AG to be a ray proceeding from the point A
and *