Biomedical Engineering Reference
In-Depth Information
We.can.apply.the.paraxial.approximation.(Equation.2.4).to.ind.the.length.
VQ
:
R QC
=
+
∆
3
2
h
R
=
QC
+
2
h
R
2
R QC VQ
−
=
=
2
.
Substituting.for.
VQ
.then.gives
(
)
n
s
n
s
n
−
n
1
1
+
2
2
=
2
1
R
.
Consider.what.happens.when.the.distance.
s
1
.becomes.very.large,.that.is,.for.an.object.at.a.very.long.
distance..In.the.limit.that.
s
1
→∞,.we.have
(
)
→ =
n
−
n
n
s
n R
2
2
2
1
2
=
s
)
=
'
f
2
(
R
n
−
n
.
2
1
Here,.the.light.comes.to.a.focus.at.a.set.distance.
f
′.into.the.media.with.index.
n
2
..his.is.deined.as.the.
focal.point.within.medium.2..Since.the.light.is.coming.from.ininity,.the.light.rays.would.be.parallel.and.
the.wavefronts.would.be.plane.waves..If.
s
2
→∞,.we.have
(
)
→ =
n
s
n
−
n
n R
1
1
=
2
1
s
1
)
=
f
(
1
R
n
−
n
.
2
1
Here,.the.light.comes.to.a.focus.at.a.set.distance.
f
.into.the.media.with.index.
n
1
..his.is.the.focal.point.
within.medium.1.
2.5 thin Lens equation
In.most.optical.systems,.we.would.like.to.have.the.light.pass.from.one.point.
s
1
.to.another.point.
s
2
,.
both.of.which.are.in.air.rather.than.inside.some.material.such.as.glass..his.is.accomplished.using.a.
thin.lens.that.has.two.curved.surfaces,.as.shown.in.Figure.2.5..Since.a.lens.is.usually.used.in.air,.we.
have.set.
n
1
.=.1.
When.describing.the.object.and.image.distances,.and.the.radii.of.curvature.of.the.two.surfaces.of.the.
lens,.the.following.conventions.for.the.signs.of.the.distances.and.radii.of.curvature.are.used.(Feynman.
1966):
P
S
1
S
2
R
O
I
V Q
V' C
n
2
FIGuRE 2.5
Refraction.at.two.curved.interfaces.to.form.a.biconvex.lens.
