Physics 1202: Lecture 23Today’s Agenda

• Announcements:– Lectures posted on:

www.phys.uconn.edu/~rcote/– HW assignments, etc.

• Homework #7:Homework #7:– Due next FridayDue next Friday

oi

fh’

h

Rh

h’o-R

R-i

oi

&

Mirror – Lens Definitions• Some important terminology we introduced last class,

– o = distance from object to mirror (or lens)– i = distance from mirror to image

o positive, i positive if on same side of mirror as o.– R = radius of curvature of spherical mirror– f = focal length, = R/2 for spherical mirrors. – Concave, Convex, and Spherical mirrors.– M = magnification, (size of image) / (size of object)

negative means inverted image

R

object

h

image

o

i

Summary• We have derived, in the paraxial (and thin lens) approximation,

the same equations for mirrors and lenses:

when the following sign conventions are used:

Variable

f > 0f < 0

o > 0o < 0

i > 0i < 0

Mirror

concaveconvex

real (front)virtual (back)

real (front) virtual (back)

Lens

convergingdiverging

real (front)virtual (back)

real (back) virtual (front)

This could be used as a projector. Small slide on big screen

This is a magnifying glass

This could be used in a camera. Big object on small film

UprightEnlargedVirtual

InvertedEnlargedReal

InvertedReducedReal

3 Cases for Converging Lenses

Image Object

Inside F

ObjectImage

Past 2F

ImageObject

BetweenF & 2F

1) Rays parallel to principal axis pass through focal point.2) Rays through center of lens are not refracted.3) Rays toward F emerge parallel to principal axis.

F

F

Object

P.A.

Image is virtual, upright and reduced.

Image

Diverging Lens Principal Rays

Lecture 23, ACT 1• A lens is used to image an object on a

screen. The right half of the lens is covered. – What is the nature of the image on the

screen?(a) left half of image disappears(b) right half of image disappears(c) entire image reduced in intensity

object

lens

screen

Multiple Lenses • We determine the effect of a system of lenses by considering the

image of one lens to be the object for the next lens.

For the first lens: o1 = +1.5, f1 = +1

For the second lens: o2 = +1, f2 = -4

f = +1 f = -4

-1 +3+10 +2 +6+5+4

Multiple Lenses • Objects of the second lens can be virtual. Let’s move the second lens

closer to the first lens (in fact, to its focus):

For the first lens: o1 = +1.5, f1 = +1

For the second lens: o2 = -2, f2 = -4

Note the negative object distance for the 2nd lens.

f = +1 f = -4

-1 +3+10 +2 +6+5+4

Multiple Lenses • If the two lenses are thin, they can be touching – i.e.

in the same position. We can treat as one lens.ftotal = ??

?

Adding,

For the first lens: o=o1, i1 and f1

For the second lens: o2 = -i1, i2=i, f2

As long as,

The Lens Equation– Convergent Lens:

if

h’o

h

The Lensmaker’s Formula• So far, we have treated lenses in terms of their focal lengths. • How do you make a lens with focal length f ?

• Start with Snell’s Law. Consider a plano-convex lens:

Snell’s Law at the curved surface:

The bend-angle is just given by:

The bend-angle also defines the focal length f:

The angle can be written in terms of R, the radius of curvature of the lens :

Putting these last equations together,

RNair air

h light ray

Assuming small angles,

More generally…Lensmaker’s Formula

Two curved surfaces…

Two arbitrary indices of refraction

R > 0 if convex when light hits it

R < 0 if concave when light hits it

The complete generalized case…

Note: for one surface Planar,

Compound Microscope

o1

h

O

I2h2

feye

h1

I1

i1

Objective(fob< 1cm)

fob

L

Eyepiece(feye~5cm)

Magnification:

Refracting Telescope

Starfeye

I2h2

fob

Objective(fob~ 250cm)

Eyepiece(feye~5cm)

i1I1

h1

AngularMagnification:

~fe

I1

eyepiece

I2

~fo

objectiveLThe

EYE

Retina

To brain

The Eye• What does the eye consist of?

– Sphere (balloon) of water.- An aperture that controls how much light gets through – the Iris/pupil- Bulge at the front – the cornea

- A variable focus lens behind the retina – the lens- A screen that is hooked up to your brain – the retina

Cornea

Iris Lens