6—12.
ELECTRON OPTICS
‘131
common focus it is necessary that the deeçting force should in—
crease in direct proportion to its distance off the axis.
We shall now see that the “index—of refraction” of an electric
eld for electron rays is directly
-
proportional to their velocity. At
‘
i
'
the
instant when electrons are
V:
.
:
entering an electric eld at an
,
|
_
angle, as
in gure 6—18, we may“
_
:
,
n: .
consider the incident velocity vl to
’
—
have a component v1x parallel to
E
,
n2
,
'
the boundary surface, and the ve|
F—
_
E
locity 112 in the eld to have a
_|
V:
similar component vzæ.
Since v_lœ
,
:
_
is unaltered by the eld, sin 7 =
'
l
02x/02 .: Ulm/Ü2- Also, sin i : Ü1z/U1FIG. 6—18.
The refraction_ of light
,
.
_
_
_
and electron rays.
Therefore sm z/ sm ? = 02/01.
.
-
But, according to Snell’s law for the refraction of light rays, this
ratio is equal to the ration 712/ 771 of the respective indices of refraction.
It follows that the,iñdex qf rcy‘mcz‘ionfar electron my: is
…
,
”_ = _)
,
,
_
.—
(6—17)
Where 0 is the
of the
in the eleCtric eld and c
»
chosen equal—“(to,3 X
For electrons wh0'3e
velocities” eXc€ed
volts,
of refraCtion is
giVen
'
,.
Ï
,,
'
n=——Ü/c————
(6—18) —
Theamount0frefractwnorbendmgwhmhan electron raye under—'
,
—
elSlsprop0rtmnalt°therat1°°fïevelœmæm thetW° elds
.
f
.
.
.
ï
0rmeasured”Inœntrastwltheusua10Ptlcalcasesthe
Index@frefractwn@felectr0nlenseslsntconstantthmughoutthe Ï