Biomedical Engineering Reference
In-Depth Information
located.at.a.distance.
S
1
.to.the.let.of.the.lens,.which.is.further.than.one.focal.length.
f
.to.the.let.of.the.lens,.
will.form.a.virtual.image.on.the.same.side.of.the.lens.at.
S
2
,.which.is.closer.than.the.focal.length..It.is.also.
possible.to.have.a.lens.with.one.convex.surface.and.one.concave.surface..his.form.of.a.lens.is.called.a.
meniscus.lens..It.is.also.possible.to.have.a.lens.with.one.side.planar.and.the.other.side.either.convex.or.
concave..hese.are.called.plano-convex.and.plano-concave.lenses,.respectively.
2.6 Magniication
Again. from.
Figure. 2.6
,. we. can. determine. the. ratio. of. heights. of. the. object. and. the. image.. We. have.
redrawn.this.igure.with.some.similar.triangles,.where.the.height.of.the.right.triangle.that.includes.the.
object.is.
y
,.and.the.height.of.the.right.triangle.that.includes.the.image.is.
y
´.(Figure.2.9).
From.the.similar.right.triangles.on.the.let-hand.side.of.the.lens,.we.can.ind.the.magniication.
M
:
y
y
f
′
→ ≡
y
y
′
=
f
=
M
S
−
f
S
−
f
.
1
1
We.can.also.use.similar.triangles.on.the.right-hand.side.of.the.lens.to.ind.that
y
f
y
′
−
y
y
′
=
S
−
f
2
=
→ ≡
M
S
f
f
.
2
Since.
y
′.is.below.the.optical.axis,.it.is.a.negative.quantity.by.convention,.we.say.that.the.magniication.
is.negative,.and.it.results.in.an.inverted.image..he.virtual.image.in
.
Figure.2.8
.
is.positive,.and.therefore,.
in.this.case,.the.magniication.is.positive.and.the.virtual.image.is.not.inverted.
Combining.these.two.equations,.we.ind
y
y
′
=
f
S
−
f
(
)
(
)
=
2
M
≡
=
→ −
S
f
S
−
f
f
2
1
2
S
−
f
f
1
S S
S f
S
f
f
f
S S
S f
S f
f S
(
S
)
−
−
+
2
= →
2
=
+
=
+
1 2
1
2
1 2
1
2
1
2
S S
S
1
1
1
1 2
= →
f
+
=
+
S
S
S
f
.
1
1
2
We.recover.Equation.2.6,.the.lensmaker's.formula.
S
1
S
2
f
f
y
Object
Real image
y
′
FIGuRE 2.9
Magniication.of.a.lens..he.height.of.the.object.is.
y
.and.that.of.the.image.is.
y
′..(Credit:.Wiki.)
