Geometrical Optics

Chapter 24

1

This week This week we begin the study of optics. I have

no idea how far we will get into these chapters. Lenses & Mirrors Interference Diffraction

Probably not enough material to justify a 7:00AM class. We can use office hours for that purpose.

There will be a quiz on Friday. Watch for a new Mastering Physics (I know you

just can’t wait!) Last quiz is in the bin.

2

From the website:

Remaining Clicker Evil

Fix this evil or you will have a ZERO clicker score!! Practice Problem Set (Monday Session)

****** TAKE NOTE OF THE FOLLOWING ******The end of the semester is approaching. The common Final Examination will be on Saturday, Dec 12, 2009

from 9AM-12PMin room PSY 108

There will be one more exam this semester but itprobably will be on December 2 (Wednesday).

This exam will cover the remaining material covered. It willalso be covered in the final exam.

Don't forget to check the evil clicker file!

3

Geometrical Optics

Yup … more angle stuff!

4

Geometrical Process

Lens orMirror

ObjectImage

Oh where, oh where, has my bug’s image gone .. oh where or where can it be???5

Where’s the image, where’s the object … who cares??? We do!

What kind of an image is it? Real Virtual

Where is the object, where is the image? Behind the lens In front of the lens

Where is the light coming from? Where is it going? What is the size of the image? (magnification) What is the orientation of the image?

Same as the object, Inverted (upside down) Reverse

Questions about the image:

6

What kind of optics: Mirror

Planar Concave Convex

Lens converging diverging

Where is the light? Have you seen the light

yet?

7

Note The object is usually the source of light. The image is where the light converges to

replicate the object. The image can be on either side of the

“optical element” The image can be real or virtual The image can form an object for a second

optical element.

Yes .. it can be confusing. We will attack this a point at a time.

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Signs

9

Signs – We mean (-) or (+) The distance from the object to the lens/mirror is

called the object distance. It is positive if it is on the same side of the optical

element as the incoming light. Otherwise it is negative It is designated by s

The distance from the image to the lens/mirror is called the image distance. It is positive if it is on the same side as the outgoing

light It is designated by s’. Otherwise it is negative.

Without this sign convention, these problems would be much more difficult. So pay attention to them!!

10

11

12

Paraxial Rays : Small Angle Approximation

sintan

sintheta sin tan

0.01 0.01 0.01

0.02 0.02 0.02

0.03 0.03 0.03

0.04 0.04 0.04

0.05 0.05 0.05

0.06 0.06 0.06

0.07 0.07 0.07

0.08 0.08 0.08

0.09 0.09 0.09

0.10 0.10 0.10

0.11 0.11 0.11

0.12 0.12 0.12

0.13 0.13 0.13

0.14 0.14 0.14

0.15 0.15 0.15

0.16 0.16 0.160.17 0.17 0.17

0.18 0.18 0.18

0.19 0.19 0.19

0.20 0.20 0.20

0.21 0.21 0.21

0.22 0.22 0.22

0.23 0.23 0.23

0.24 0.24 0.24

0.25 0.25 0.26

0.26 0.26 0.27

0.27 0.27 0.28

0.28 0.28 0.29

0.29 0.29 0.30

0.30 0.30 0.31

13

'

1'

ss

y

ym

14

15

Curved Mirrors

For Student Misery Only!

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Concave Mirror

con-CAVE

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Sign Convention

When the Center of Curvatureis on the same side of theoutgoing ray, R is positive.

Otherwise, if the center of curvature is not on the same sideas the outgoing ray, R is negative.

18

Concave Mirror/Paraxial Approximation

2

2'

'

s

h

s

hs

h

s

h

The normal to thesurface passes

through C

Therefore

R

h

Consequently

Rss

R

h

s

h

s

h

2

'

11

2

'

MIRROREQUATION

19

For this structure

A. The Radius R is positive and s’ is negativeB. The Radius R is negative and s’ is negativeC. R is positive and s’ is positiveD. R is negative and s’ is positive

Answer20

When the Center of Curvatureis on the same side of theoutgoing ray, R is positive.

the image distance is positive if it is on the same side as the outgoing light

21

What about here? R, s, s’ (convex mirror)

22

Concept: Focal Length of a Mirror

23

fss

sRss

1

'

112

Rs'f

0)(1/s

2

'

11

Going Backwards

24

'

0'

1

)2

(1/s 2

2

'

11

ss

R

Rs

Rss

More Better – A Parabola

25

surveillance

Image Formation

26

0'

0

0

s

R

s

‘

‘

y’<0(from the diagram) so image is inverted.

The geometry……

27

s

s'-m

and '

'

s

y

so Triangles,Similar

diagram)in image inverted fromsign (- '

s

y

y

ym

A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 15 cm from the mirror.

28

10 cm 5 cm

Normal to mirrorand bounces backalong incomingpath.

mmys

sm

s

fRss

4

5.'

5.7'

12

'

11

A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 10 cm from the mirror.

29

10 cm 5 cm

mmys

sm

cms

fRss

8

0.1'

10'

12

'

11

A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 2.5 cm from the mirror.

30

10 cm 5 cm

eyemmys

sm

cms

fRss

8

0.2'

5'

12

'

11

virtualimage