Principles of Geometric Optics - Adaptive Optics for Biological Imaging - page 37

Substituting.for.the.focal.length. f .in.Equation.2.5,.we.have

1 1 1

+ = (2.6)

s s f

. .

1 2

his.is.called.the.lensmaker's.equation,.which.provides.a.relationship.between.the.focal.length. f .and.
the.distances.to.the.object.and.the.image..If.both.the.object.and.the.image.distances. s 1 .and. s 2 ,.respec-
tively,.are.equal,.then.for. s 1 .= s 2 .=. s :

1 1 2 1

s f

+ = = → = 2

s s s f

.

In.general,.the.object.and.the.image.may.not.be.points,.as.shown.in . Figure.2.5 ,. but.rather.extended.
objects,.as.shown.in.Figure.2.6..Here.the.object.is.shown.as.an.arrow.that.extends.above.the.optical.axis..
We.can.ind.out.where.the.image.is.positioned.by.considering.two.principal.light.rays,.one.from.the.tip.
of.the.object.that.is.parallel.to.the.optical.axis.and.one.from.the.tip.of.the.object.that.passes.through.
the.center.of.the.lens..his.is.called.ray.tracing..he.light.ray.from.the.tip.of.the.object.that.is.parallel.to.
the.optical.axis.is.equivalent.to.a.light.ray.from.ininity,.and.therefore,.ater.passing.through.the.lens,.
it.will.intersect.the.optical.axis.on.the.right-hand.side.of.the.lens.at.the.focal.point. f ..he.light.ray.that.
passes.through.the.center.of.the.lens.has.a.symmetric.optical.path.through.the.thin.lens,.and.therefore.
it.can be.drawn.as.a.straight.line..his.ray.will.be.refracted.by.a.certain.amount.in.traveling.from.air,.
with. n .= n 1 =.1,.into.the.glass.with. n .=. n 2 ,.with.the.delection.being.given.by.Snell's.law,.as.described.
in. Equation. 2.3.. his. light. ray. will. be. refracted. a. second. time. when. it. exits. the. lens,. and. therefore. it.
will.continue.along.the.same.direction.ater.passing.through.the.lens..For.a.thin.lens,.we.can.draw.that.
ray.as.a.straight.line..Where.these.two.rays.intersect.on.the.right-hand.side.of.the.lens,.an.image.will.
be.formed..Since.this.image.is.on.the.opposite.side.of.the.lens.from.the.object,.it.is.called.a.real.image..
If a.screen.were.to.be.placed.at.this.location,.an.image.of.the.object.would.be.seen,.although.the.image.
is.inverted.(i.e.,.upside.down),.and.the.arrow.in.the.image.may.be.diferent.in.length.from.the.arrow.
shown.as.the.object..We.will.discuss.this.in . Section.2.6 , .when.we.consider.the.magniication.of.the.lens..

S 1 S 2

f f

Object

Real image

FIGuRE 2.6 Ray. tracing. to. ind. the. object. and. the. image. for. a. thin. biconvex. lens.. he. object. is. located. at. a.
distance. S 1 .to.the.let.of.the.lens,.and.the.image.is.located.at.a.distance. S 2 .to.the.right.of.the.lens..he.position.of.
the.image.can.be.found.by.inding.the.intersection.of.two.light.rays.emanating.from.the.tip.of.the.object..hree.
.principal.light.rays.are.shown..One.passes.through.the.focal.point.on.the.let-hand.side.of.the.lens,.while.another.
passes.through.the.focal.point.on.the.right-hand.side.of.the.lens..hese.light.rays.appear.to.come.in.from.ininity..
A.third.light.ray.passes.through.the.center.of.the.lens..Since.the.lens.is.considered.to.be.a.thin.lens,.this.light.ray.is.
drawn.as.a.straight.line.from.the.tip.of.the.object.to.the.tip.of.the.image..(Credit:.Wiki.)