1. Lenses, mirrors and refractive surfaces
Friday Sept. 13, 2002

2. Refraction at a spherical interface: Paraxial ray approximation
Snell’s law
____________________________
Leads to…
Governs refraction at an interface
All rays from O pass through I, i.e. I = image of O
For a given object distance s, can find a conjugate distance s’

3. Definitions: Focal points of a curved interface
Governs refraction at an interface
Focal Points:
Suppose object at s = 
All rays arriving at lens will travel parallel to optic axis and,
This defines the second focal point

4. Definition: Focal points of a curved interface

5. Definitions: Focal points of a curved interface
Suppose image at s’ = 
All rays leaving lens will travel parallel to optic axis and,
This defines the first focal point.

6. Focal points for curved interface
Show
Definition: Focal points, f, f’ are conjugate with s, s’ = 

7. Definitions: Power n’>n Power of surface
P > 0 for converging surface C n n’ C n n’
R<0
P < 0 for diverging surface

8. Definitions: Power Thus if n’ > n and R< 0 In general,
 f, f’, and P are all negative
In general,

9. Refraction at a spherical interface
In paraxial ray approximation: Imaging occurs according to:

10. Object-image height relationship

11. Lateral Magnification
Since h is negative
True for all imaging according to

12. Lateral magnificationh R C h’ n n’ s s’
In above, since s, s’ > 0  m < 0  inverted image
New image shown in figure is
real (light actually passes through)
inverted
demagnified or reduced

13. Thin lenses Treat as two spherical interfaces
Assume that the lens thickness t is negligible n n’ O I C2 C1 nL R1 R2 s s’

14. Thin lens: First surfaceP’ P V R1
s, R1 > 0 s s”
s” < 0 since to the left of V

15. Thin lens: Second surfaceP’ t nL s” s’

16. Thin lens: second interface
First interface
Second interface
Object distance t + s” = t - |s”|
Thin lens  t → 0, so object distance = - |s”|

17. Thin lens
First interface
Second interface

18. Thin lens
In a single medium (n=n’)
In air (n = 1)
Lens makers formula

19. Thin lens (nL=1.5): Examples
Double convex lens
|R1| = |R2| = 20 cm
f =____ P = _____
Double concave lens
Plano-convex

20. Thin lens: Power
Thicker in middle
P > 0
Thinner in middle
P < 0

21. Thin lens: Ray diagrams

22. Reflection at a curved mirror interface in paraxial approx.y   φ ’  O C I s’ s

23. Reflection at a curved mirror interface
Show that: