EXAMS:

There will be two 75-minute evening exams and a two-hour final exam. The evening exams

are multiple-choice and should be able to be completed within 75 minutes by a well-prepared

student; note that we’re giving you 120 minutes. The times and locations of the evening

exams are as follows:

Exam 1: Wednesday, February 13 @ 8 – 10 PM in Physics 203 and Physics 331

Exam 2: Tuesday, March 26 @ 8 – 10 PM in Physics 114

All exams are closed book. For the exams you will need a #2 pencil, a calculator and your

student ID. You may make a single crib sheet for Exam 1 (you may write on both sides of an

8.5” x 11” sheet of paper). Bring this and a second crib sheet to Exam 2; bring both crib

sheets and a third to the Final Exam. Many, but not all, formulae will be provided on the front

of the Exams.

PHYS 219 General Physics: Electricity, Light

and Modern Physics

Exam 2 is scheduled on Tuesday, March 26 @ 8 – 10 PM In Physics 114

It will cover four Chapters 21, 22, 23, and 24.

Start reviewing lecture notes, home works, and recitation problems !

Chapter 24 Geometrical Optics – Lecture 17

24.1 Ray (Geometrical) Optics

24.2 Reflection from a Plane Mirror

24.3 Refraction

24.4 Reflections and Images Produced by Curved Mirrors

24.5 Lenses

24.6 How the Eye Works

24.7 Optics in the Atmosphere

24.8 Aberrations

Image From a Concave Mirror – Examples

Section 24.4

Drawing A Ray Diagram

• Three rays are particularly easy to draw

(1) Focal ray

(2) Parallel ray

(3) Central ray

• The focal ray

• From the tip of the object through the focal point

• Reflects parallel to the principal axis

Section 24.4

Drawing A Ray Diagram, cont.

• The parallel ray

• From the tip of the object parallel to the principal axis

• Reflects through the focal point

• The central ray

• From the tip of the object through the center of

curvature of the mirror

• Reflects back on itself

• The three rays intersect

at the tip of the image

Section 24.4

Properties of an Image

• Magnification is the ratio of the height of the image,

hi, to the height of the object, ho

• By convention, the image height of an inverted

image is negative

• Therefore, the magnification is also negative

Section 24.4

i

o

hm

h=

Concave Mirror and Virtual Images

• Use ray tracing to find the image

when the object is close to the mirror

• Closer than the focal point

• Use the same three rays

• The rays do not intersect at any

point in the front of the mirror Section 24.4

Virtual Images

• Extrapolate the rays back behind the mirror

• They intersect at a single image point

• The rays appear to emanate from the image point

behind the mirror

• The image is virtual because light does not actually

pass through any point

on the image

• The object and its image

are on different sides of

the mirror

• The image is upright and

enlarged Section 24.4

Demo - Two Concave Mirrors and a Pig

Demo - Two Concave Mirrors and a Pig

• Real image from two concave mirrors

Ray Tracing – Convex Spherical Mirrors

• A mirror that curves away

from the object is called a

convex mirror

• The center of curvature and

the focal point lie behind the

mirror

• After striking the convex

surface, the reflected rays

diverge from the mirror axis

• The parallel rays converge

on an image point behind

the mirror

• This is the focal point, F

Section 24.4

Ray Tracing – Convex Mirrors, cont.

• The same three rays

are used as were used

for concave mirrors

• The focal ray is directed

toward the focal point

but is reflected at the

mirror’s surface, so

doesn’t go through F

• The three rays

extrapolate to a point

behind the mirror

• Produces virtual image

Section 24.4

Mirror Equation and Focal Length – A Concave Mirror

Section 24.4

0 0 0 0

0 0 0 0

00 0

0

0 0 0

0 0

0

/ /,

/ ( ) / ( )

( ) ( )

1 1 22

1 1 2

2

i i i i

i i i i

ii i

i

i i i

i i

i

i

i

h h h h h s h s

s s s R R s h s R h R s

R s s Rs R s s s R

s s

s R s s s s s R

s R s R s ss s R

Rs f f

s R

f is the focal length

f >0 for a conave

mirror

f <0 for a convex

mirror

Mirror Equation and Magnification

• The mirror equation can be written in terms of the

focal length

• The magnification can also be found from the similar

triangles shown in fig. 24.30

o is s+ =

1 1 1

ƒ

Section 24.4

f is the focal length

f >0 for a conave mirror

f <0 for a convex mirror

i i

o o

h sm

h s

Sign Convention, Summary

Section 24.4

Lenses

• A lens uses refraction to form an image

• Typical lenses are composed of glass or plastic

• The refraction of the light rays as they pass from the

air into the lens and then back into the air causes the

rays to be redirected

• Although refraction occurs at both surfaces of the lens,

for simplicity the rays are drawn to the center of the

lens

Section 24.5

Lenses, Focal Point

• Parts B and C show the simplification of the single

deflection of the rays

• Parallel rays close to the principal axis intersect at

the focal point

• This is true for incident rays from either side of the lens

• The focal points are at equal distances on the two sides of

the lens

Section 24.5

Spherical Lenses

• The simplest lenses

have spherical surfaces

• The radii of curvature of

the lenses are called R1

and R2

• The radii are not

necessarily equal

Section 24.5

Types of Lenses

• Converging lenses

• All the incoming rays parallel to the principal axis intersect

at the focal point on the opposite side

• Diverging lenses

• All the incoming rays parallel to the principal axis intersect

at the focal point on the same side as the incident rays

Section 24.5

Focal Point – Diverging Lens

• The parallel incident

rays from the left are

refracted away from the

axis

• The rays diverge after

passing through the lens

• The rays on the right

appear to emanate from

a point F on the left side

of the lens

• This point F is one of

the focal points of the

lens Section 24.5

Image from a Converging Lens

• Ray tracing analysis

can be used to find the

image

• An infinite number of

rays emanate from the

object

• For simplicity, choose

three rays that are easy

to draw

• Start at the tip of the

object

Section 24.5

Rays for a Converging Lens

• The parallel ray is initially

parallel to the principal

axis

• Refracts and passes

through the focal point on

the right (FR)

• The focal ray passes

through the focal point on

the left (FL)

• Refracts and goes parallel

to the principal axis on the

right

• The center ray passes

through the center of the

lens, C Section 24.5

Rays, cont.

• If the lens is very thin, the center ray is not deflected

by the lens

• These three rays come together at the tip of the

image on the right of the lens

• In this case, the image is inverted

• The image is real

• The rays pass through the image

Section 24.5

Ray Tracing – Diverging Lens

• Follow the rules for ray

tracing for lenses

• Since the refracted rays

do not intersect on the

right side of the lens,

extrapolate the rays

back to the left side of

the lens

• The extrapolations do

intersect

• The point of intersection

is the image point at the

tip of the image Section 24.5

Sign Conventions for Lenses, Summary

Section 24.5

/ /,

/ / ( )

( )

1 1 1

o i o i o o i i

o i i o i i

ii o i

o i

i o o i

o i

h h h h h s h s

s s f s f h f h s f

s ffor s f s s f

s s

or s f s f s ss s f

Thin-Lens Equation

thin-lens equation

The shaded

triangles are

similar triangles

Thin-Lens Equation and Magnification

• The thin-lens equation is

found from an analysis of

the similar triangles

• The magnification can also

be found from the similar

triangles shown

• These results are identical

to the results found for

mirrors

o is s+ =

1 1 1

ƒ

Section 24.5

i i

o o

h sm

h s

The Human Eye (1)

≈ 2.5 cm

Refraction at the cornea and lens surfaces produces an inverted real image on the retina of the eye (the brain interprets it upright !)

For an object to be seen clearly, the image must be formed at the location of the retina

The shape of the lens controls the distance of the image

• The lens is held in place by ligamen that connect it to the ciliary muscle that allows the lens to change shape and thus change the focus of the lens

• The index of refraction of the fluids in the eye are close to that of water with a value of 1.34; the index of refraction of the material making up the lens is 1.40

• Thus most of the refraction occurs at the air/cornea boundary.

The Human Eye (2)

≈ 2.5 cm

The Human Eye (3)

≈ 2.5 cm

0

1 1 1

id d f

f depends on d0

d0 ↓ => f↓ to keep di at ≈ 2.5 cm

Example: Corrective Lenses (1)

Question: A hyperopic (far-sighted) person whose uncorrected near point is 75 cm wishes to read a newspaper at a distance of 25 cm. What is the power of the corrective lens needed for this person?

Answer:

• The corrective lens must produce a virtual, upright image of the newspaper at the near point of the person’s vision as shown below

• The object and image are on the same side so the image distance is negative

Example: Corrective Lenses (2)

• Thus the object distance is 25 cm and image distance is -75 cm

• The required lens is a converging lens with a power of +2.66 diopters or +2.66 D (focal length of +0.376 m = 1/ 2.66 D)

1 1 12.66 D

0.25 m 0.75 m f 0

1 1 1

id d f

Demos

Coin Illusion 7A-11

Images formed by Lenses 7A-30

Eye Model 7A-33