Geometrical Optics – Part II

Geometrical Optics – Part II

Chapter 24

1

Going Backwards

2

'

0'

1

)2

(1/s 2

2

'

11

ss

R

Rs

Rss

Stuff We continue with mirrors and lenses and even

refractive surfaces. Quiz on Friday For a while, office hours will be in, of all

places, my office. We really don’t need MAP-318 except before exams. And the hours are too confusing.

Next Exam is on Wednesday, December 2nd. I give up on the remaining evil clickers.

Clicker grade=0. Let’s move on.

3

4

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

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

Concave Mirror/Paraxial Approximation

Consequently

Rss

R

h

s

h

s

h

2

'

11

2

'

MIRROREQUATION

5

Image Formation

6

0'

0

0

s

R

s

‘

‘

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

The geometry……

7

s

s'-m

and '

'

s

y

so Triangles,Similar

diagram)in image inverted fromsign (- '

s

y

y

ym

Let’s try an example

8

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.

9

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.

10

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.

11

10 cm 5 cm

eyemmys

sm

cms

fRss

8

0.2'

5'

12

'

11

virtualimage

The Concave Mirror

12

More Convex Mirror

13

Graphical Methods are very useful to check your work.

14

Moving on to refractive surfaces

15

Spherical Refractive Surfaces

16

air glass

A closer look atthe Math ….

17

bbaa

b

a

nn

)(

'

s

h

b

a

b

aab n

n

n

nR

h

s

h

Ignoring

R

nn

s

n

s

nR

hnn

s

hn

s

hn

bnnn

nnnn

n

n

abba

abba

baab

aabb

b

a

)(

'

)('

)(

)(

No for the height of the image

18

sn

sn

y

ym

s

ynn

s

ynn

s

ys

y

s

a

bbbaaa

b

aa

'''

''

'

tan

Check this out – how big is R?

19

From the math:

20

0'

)(

'

s

n

s

nR

nn

s

n

s

n

ba

abba

sn

sn

y

ym

s

a ''

1

1'

''

0'

m

sn

sn

snsns

n

s

ns

n

s

n

a

b

ba

ba

ba

The Thin Lens We ignore the

thickness of the lens.

We will use mostly geometrical methods.

Any ray that bends is assumed to bend only once at the center of the lens.

22

From whence it came

23

Surface 1

Surface 2

n=1 n=1.5 n=1

Surface 2n>1

The thin lens - geometry

24

parallel

More Geometry

Lens is thin Actual thickness of the lens is ignored.

Image from first surface provides the object for the second surface.

Paraxial Ray Approximation sin(x)=tan(x)=x cos(x)=1 x is in RADIANS

25

More Geometry

26

Triangle PQO andtriangle P’Q’O aresimilar.

s

s

y

y ''

We will show that fora very thin lens:

F1=F2=f

fss

s

sm

f

fs

y

y

or

fs

y

f

y

1

'

11

'''

'

'

AOP'at Looking

The Thin Lens Equation

27

This, of coursedepends on where the

object is placed with respect to f.

Thin Lens (con’t)

28

Image thatwould form

if material “a”was all on this

side of the lens.

Object for secondsurface.

29

Procedure for equation

•Solve for image position for first surface•Use image as object for the second surface.•Use the refraction equation in both cases.

222

b

111

a

's

n

:surface secondFor

's

n

:#1 SurfaceConsider

R

nn

s

n

R

nn

s

n

bcc

abb

For a lens. na=nc=1So we can call the middle one just n

12 ' : ssNote

Mess with the algebra and you will get:

221

111

1

'

1

s'

n-

1

's

1

R

n

s

R

n

s

n

FINALLY – with some algebra and obvious substitutions, we get:

30

fRRn

ss

111)1(

'

11

21

The Lensmaker’s Equation

Two Ways to do this STUFF Algebraically using the lens equation (with the

1/f if you know it) Using graphical Methods

31

Graphical Methods:

32

Graphical Methods:

33

Most important case: converging lensObject to left of F1

34

Most important case: converging lens

35


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Geometrical Optics – Part II

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Transcript of Geometrical Optics – Part II