chapter 4 thin lenses

Homework for chapters 4 and 5

• Chapter 4: 3, 4, 8, 12, 13, 14, 16

• Chapter 5: 3, 4, 5, 6, 11, 12, 15,16

• Due next Tuesday before class

Thin Lenses and Their Foci

How thin is thin?

When thickness << all

relevant distances

Primary foci Fs

Secondary foci F’s

Focal lengths

f=f’ for thin lenses

In air (uniform medium)

Focal plane and chief ray

• Parallel rays are

focused at the focal

plane

• Chief ray does not • Chief ray does not

deflect in thin lenses

Image Formation

All relevant rays from one point (object) go to

another point (image)

Conjugate points and planesTo find an image

1. By graph

2. By experiment

3. By calculation

Lens formula

1 1 1

's s f+ =

Equivalent of Gaussian equation

Sign convention

• All from left to right

• Up is positive for object and image dimensions

Left Right

s + -s + -

s’ - +

f + -

f’ - +

r - +

Graphical-parallel rays

• 4//1, refraction goes through F’

• 5 is the chief ray

• 6 goes through F, refraction parallel to 1

• 4, 5, and 6 meet at Q’

Graphical-parallel rays 2

• 4//1, refraction 5 imaginably goes through F’

• 6 imaginably goes through F, refraction 7

parallel to 1

• 8 is the chief ray

• 5,6 and 8 meet at Q’, virtual image

Graphical-oblique ray

• Arbitrary ray 3 from object M meets lens at R

• Chief ray 5//3

• 5 meets secondary focal plane at X

• 6 goes through T and X and meets 1 at M’

Lens Formula

s=6.0 cm, f=4.0 cm, what is s’?

1 1 1

's s f+ = '

sfs

s f=

−

s’=+12.0 cm can be checked easily by the graphical method

Lateral magnification

' ' '

' ' '

M Q A M

M Q A M

y M Q

y M Q

=

==

' 'y sm

y s= = −

Virtual Images

s=6.0 cm, f=10.0 cm, what is s’&m? s=12.0 cm, f=-6.0 cm, what is s’&m?

6 10' 15

6 10

' 152.5

6

sfs cm

s f

sm

s

= = = −− −

−= − = − = +

i 12 ( 6)' 4.0

12 ( 6)

' 4 1

12 3

sfs cm

s f

sm

s

−= = = −− − −

−= − = − = +

i

Lens Maker’s equation

1 1 ( 1)

1 1' 12 1'

1 1 (1 )

n

s s rs s

n

−+ =

= −−

1 2

1 1 1( 1)( )

1 1 1

nf r r

= − −

+ =

1 2 1 2

1 1 (1 )

1' 2 ' 21 1 1 1

( 1)( )'

n

s s r

ns s r r

−+ =−

+ = − −

1 1 1

's s f+ =

Gaussian form of lens formula

Lens Maker’s equation-an example

1 2

1 1 1( 1)( )n

f r r= − −

Want to make plano-convex

lens f=25.0 cm. Glass has

n=1.520, find radius of

curvature.

Thin lens combinations-by formulae

1 1 1

1 1 1

2 1

2 2 2

1 1 1

'

If the distance between lenses is

'

1 1 1

'

s s f

d

s d s

s s f

+ =

= −

+ =

Thin lens combinations-parallel rays

Thin lens combinations-oblique rays

Object space and image space

Both spaces occupy the whole space

All rays from the object occupy the object space

All rays forming the image occupy image space

4 is in the object space

7 is in the image space of the 1st lens but in the object space of the 2nd lens

M1’ is in the image space of lens 1 and the object space of lens 2

10 is in the image space of the second lens.

Power of thin lenses

1 2

1 1 1( 1)( )P n

f r r= = − −

Measured in diopters (number when f is measured in meters)

Thin lens in contact

1 1 1

2 1 1

1 1 1

'

If the distance between lenses is 0

' '

1 1 1

s s f

d

s d s s

+ =

== − = −

− + =1 2 2

1 21 2 1 2

1 2

1 1 1

' '

1 1 1 1

'

1 1 1 1 1

'

s s f

P Ps s f f

s s f f f

− + =

+ = + = +

+ = + =

Lens Formula-Newtonian

2

'

'

'

'

y y

x f

y y

x f

xx f

−=

−=

=

Hyperbolic equation

Both negative or both positive

Careful with negative f

Exercises

Lens makers formula-3 media

1 1 1

' ( ' )

'

' '' ( '' ')

' ''

n n n n

s s r

n n n n

s s r

−+ =

−+ =2 2 2

2 1

1 2 1 2

' ''

' '

We thus have

'' ( ' ) ( '' ')

''

s s r

s s

n n n n n n

s s r r

+ =

= −

− −+ = +

1 2

1 2

Define

'' ( ' ) ( '' ')

''

We have

''

''

If n=n'', then

n n n n n n

f f r r

n n n

s s f

− −= = +

+ =

1 2

1 1 1

s s f+ =