Biomedical Engineering Reference
In-Depth Information
.
1.. he.object.distance.
s
1
.is.positive.if.the.point.
O
.is.to.the.let.of.the.lens.and.is.negative.if.the.point.
is.to.the.right.of.the.lens.
.
2.. he.image.distance.
s
2
.is.positive.if.the.point.
I
.is.to.the.right.of.the.lens.and.is.negative.if.the.point.
is.to.the.let.of.the.lens.
.
3.. he.radius.of.curvature.of.the.lens.is.positive.if.the.center.of.the.radius.of.curvature.is.to.the.right.
of.the.lens.and.is.negative.if.the.center.is.to.the.let.of.the.lens.
For.the.example.shown.in
.
Figure.2.5
,
.both.
s
1
.and.
s
2
.are.positive..he.radius.of.curvature.on.the.let-
hand.side.of.the.lens.is.positive.and.that.on.the.right-hand.side.of.the.lens.is.negative..Since.this.lens.has.
two.convex.surfaces,.it.is.called.a.biconvex.lens.
To.solve.the.lens.equation,.we.again.calculate.the.travel.times.for.two.diferent.paths—direct.from.
point.
O
.to.
I
.and.from.point.
O
.to.
P
.and.from.
P
.to.
I
—and.equate.them..he.travel.time.along.the.straight.
path.between.
O
.and.
I
.is.given.by.the.sum.of.the.travel.times.along.segments.
OV
,.
VQ
,.
QV
´,.and.
V
´
I
:
1
1
n
c
VQ t
n
c
QV t
t
=
c
OV t
=
=
'
=
c
V I
'
OV
VQ
QV
'
V I
'
.
hen.the.total.travel.times.along.paths.
OPI
.and.
OI
.are
1
1
t
=
c
OP
+
c
PI
OPI
1
n
c
VQ QV
(
)
+
(
)
t
=
c
OV V I
+
'
+
'
OI
.
We.can.then.use.the.paraxial.approximation.(Equation.2.4).to.simplify.this.equation:
OP OQ
=
+
∆
=
OV VQ
+
+
∆
1
1
h
s
2
=
OV VQ
+
+
2
1
PI QI
=
+
∆
=
QV V
'
+
'
I
+
∆
2
2
h
s
2
=
QV V I
'
+
'
+
2
.
2
he.diference.in.the.travel.times.along.the.two.diferent.routes.would.be
1
n
c
VQ QV
(
)
−
(
)
t
−
t
=
c
OP PI OV V I
+
−
−
'
+
'
OPI
OI
−
1
h
s
2
h
s
2
n
−
1
(
)
=
+
VQ QV
'
+
2
2
c
c
.
1
2
If.the.magnitude.of.the.radius.of.curvature.on.both.sides.of.the.lens.is.the.same,.then.we.have
h
R
2
VQ QV
=
'
=
.
2
