1000000031

Ihough in

I<r,

J :gree than they did befoTe, aou \ViU

rmct .. [ :

but iC ou

gl~C,

has l;t:n in t"oir

'"' y,

th .y

w ould h:\\"c met

M ;.

"':leo paralld '"ys, (No.

~t.)

dja,

Cmo,

.le,

f,,1I

o?on~a

con!:ave mirrour

(which is nat tranfparenr,

hut hlS only

th~

furf.lce

AiJlJ

of. elear polifh.) ,hey

" 'ill be relletlod back fro:n that mirrour, and

Olee'

io a

r oint "'.

hal , the diChoce <lf the Curface of the miro

rour from

the centre of itS concavity ; for they \ViII be

rcO.-:\.qcd at as

gre¡t aD

angle

from

a perpendicu lar to the

(urfaee of tbe mirrour, as tbey fell upon it with regard

t ha! perpendicular, but on the other ud: thereof.

Tllus, Jet

be the centre of

cOnCa\'lty

of (h"e mirrour

A bO;

and let the paraUel rayo

dja,

Cm••

and

.le,

f.1I up·

at [he

points

6, and

Draw [he lines

Cid"

Cmh,

and

Che,

from the "entre

tO theCe poiotS ; and

.11

thef. lines \ViII be perpendicular to the furrace of ,he

mi~rour;

be<:aufe ,hey procced ihereto I,ke

many radii

or fpokes (rom itS cenrre. Mak. the angle

Cah

equal to

the angle

daC,

and dra\V

,he

line

amb,

wbieh will be

,he dirca ion of ,he

...

dja,

aC,er it is

rc ~céled

from ,he

poio,

of 'the mirrour; fo that ,he aogle of mcidence

.idC,

i. equal 'o the aogle of

r~fl<élioo

Cah;

the rays

m.kin~

eqnl angles witb the perpendicular

Cía

i,s

oppoTi,. fides.

Dra\V alfo the r.erpeodicular

Che

to ,h. poiot

\Vhere

[he rayo

(le

[ouches the nlirrour

and, having made the

angl:

Cci

equa1

;:0

the angle

Cee,

draw

the

lioe

cmi,

which

will be the courfe of the ray

d e,

af,er i, i. refleéled from

the

mirrour.

Tile ray

Cm.

paffing Ihrough the «otre of cooenity

of the mirrour. aod fallíog upoo i, at 6, is porpeodicular

to it; aod is therefore refteéled back from it iD the Came

lioe

bmC.

AII theCe reJleéled rayo

me~t

io the poiol

aod io

,hat point the image of the body which emi" the paral.

'el rayo

da,

Ch,

aod __, will be formed ; which point i.

di!!aot from the mirrour equal 'o half the radius

blllC

its

concaviry ..

The rayo which proceed from aoy eele!!ial objcl! may

be e!!eemed ' parallel at ,he earth; ami ,herefore, the i·

Illage. of ,hat oujea will be formed at

fIt.

when the re·

IIcéling furface of the coocave mirrour is turoed direélly

tcwards the objeél. Heoee, ,he focus

fIt

uf parallel ray'

oot in ,he centre of the mirrour's cODcavity,

bUl

half

way

between thc: mirrour and

that

centre.

Th~

"ys whieh proceed from any remote

ter~e!!rial

ob–

jeél, are oearly paraUel at the mirtour; not !!riélly fo, but

come divcr&icg to

¡1,

in reparate pencils, or, as

were,

bundles

ray.,.from each poiot of the fide

the objeél

next ,he mirrour

and therefore they

will

not be

conv.er

–

ged lO a poiot at ,he dillaoce,of half the radius of the

mirrour's conca,'ity from

ies

refteEting furface, but

ioto

fe–

parate poio.. at a Jiltle gre.ter diClaoce from the mir–

.rour:_ Acd the "earer the objeft

to the mirrour, lhe

f.rther Ihefe

poiot~

willl¡e from il ; aod an ioverted i·

·mage of the objel! \ViII be formed io them, which will

feem 'o hang peodaot. iD ,he air; and \ViII be (eeo by

eye placed bcyood ít (with regard to the mirrou r)

all refreéls like tbe objel!, and as di!!ioél as the objeél

:;úelf.

Lct

.AclJ.

(No. 22. ) be

th~

refl,éliog furf.lce of a mir–

rou r, who(e centre of concaviry is at

C¡

and let the up–

right ohjet!

D i!

be placed beyond ,he ceotre

and fend

out a conical peDcil o f diverging rays from its upper ex–

tremity

to c\'ery porot of the CODcave farface of th::

mirrour

ÁclJ.

Sut

avoid confufion, \Ve ooly draw

,liree ray' of ,hJl peocil. as

D A. De, DO .

FroOl [he centre of concavity

drtw rhe three rioht

lioes

C;f, Ce, CR,

tauching the mirraur in the

fa~e

points \Vhere the forefaid rays toueh it ; aod all thele

lines \ViII be perpendicular to the f..rfaee of ,he mirrour.

M ak. ¡he aogle

CAd

equll to ,he anglo

D AC.

and

draw the Tigbt line

for ',he eourfe of ,he refle[,ed r. y

,1:

m. ke th . angle

Ccd

equal tO the aogle

DcC.

aoJ

'draw the right lioe e"-for ,he courCe of ,he relleéled

.al

Dd:

make al fo ,he aogle

CBd

equa! to ,he aogle

DOC,

and draw ,he right lioe

for the eourfe of the refi.éled

ray

DO.

AlI,hefe reBeél.d rayo will 0yeet io the poir.t

where they will fllrm the extremity

of lhe invl!rtc.l

imago

_d.

umilar to tbe extremity

of the upTight ob.

jett

D E.

lf ,he peocíl of rayo

Eg, Eh,

be alCo eootioued to <he

mirrour, and thei r aogles of reBta ion from it be mad:

equal

their angles of incidence upon it, as

the for–

mer penci! from

lhey will .11 meet at ,he poiot _ by

rC~t:étion,

and form the extremity

of lhe image

ed,

fi–

m", r 'o ,he ex,remity

of the obj eél

DE.

And as each io,ermediare poiot of the objel!, be,weeo

and

feods ou' a peoci! of rays in like maooer to

every part of the mirrour, ,he rayo of each penci! will

be refleéled back from ir, .od meet iD all,he iotermediate

~oints

between rhe extremities

and

dof

the image; and

lo the wbol. image

will

be formed, not at

half the

dinaDCe

of the Dlirrour

from ¡ts

centre of concavity

¡'üt at a grea,er diClaoce. between

and the objeél

DE;

and the image \ViII be inverted with refpea

,he objel!.

This bcing \Vell uoder!!ood, the reader will e.lily fee

how the image is formed by ,he large

conc.ve

mirrour of

the refieéling ,e1efcope, wheo he Comes 'o the defcriptioo

of th.t ioll rumeot.

When the objeét

more remote from lhe mirrour

thao ilS centre of eoocavity

the image \ViII be leC.

thao ,he objet!o aod bc,wecn the objeEt and mirrour:

WhCR

the

objeél is nearer than the ceDtre

coocavity.

the imago \ViII be more remote aod bigger than the oh_

jeEt: thus, if

be the objeEt,

,ti

will be ilS image :

for,

the obj etl reades from the mirrour, the image

approaches nearer to it ; and

the o:'jetl approaches

ncarer

the mirrour, lhe im2ge recedes farther from

ir;

aceouot of the lelfer or gre.ter di.ergeocy of the

peocil. of rays which proceed from the objea: for, the

lefs they diverge, ,he foooer they are converged

poiolS

by refleélion ; aod the more they diverge, the fanher

they mull be refleéled before they mee!.

If the radiu. of ,he mirrour's cooeavi,y, and the dif–

tance of theobjeél from it, be kno,"o, ,he dillaoce orthe

image from ,he mirrour i. fouod by this rule ; Divide the

produa of the dirIaoce aod radius by double the di!!aoce

made lefs by the .dius, aod ,he quotieot is the dilhnce

rcquired.

the objeél be iD the ceotre of the mirrour's eon–

cavitYt