1. Optics for Residents Amy Nau O.D., F.A.A.O
Spherical Thin Lenses
Optics for Residents
Amy Nau O.D., F.A.A.O

2. Spherical Lenses Formulas
Thin lens formula 1/do+1/di=1/f F=1/f2
Linear Mag Image size/Object size= di/do
Prentice’s Rule P=F (diopters) xd (cm)

3. Thin Spherical Lenses
The shape of the refracting surface determines the type of lens and power
Object space
Image space
Image space
Object space C2 C2 C1 C1 A1 A2 A1 A2
Lens is thin if the thickness is small enough not to influence the power
All refraction is thus considered to occur in one plane between the two surfaces
A1 front surface vertex; A2 back surface vertex

4. Thin Lens Power F1=nlens-nobject/r and F2=nimage-nlens/r
The total dioptric power of the lens (F) is F1+F2
By substitution, another way to write this is : F=(n’-n)/(1/r1-1/r2) This is called the Lens Makers Formula, and it assumes that the surrounding media is air.

5. Thin Lens Problem
A plastic biconcave lens (n=1.49) has a surface radii of 40cm and 20 cm. Calculate the surface and total lens powers.
Solve for F1
F1=nlens-nobject/r
Solve for F2
F2=nimage-nlens/r
Solve for total power
F=F1+F2

6. Image Object Relationships: Position
Assumptions:
surrounding media is air
Imaging occurs through single plane
Formulas
The Gaussian Imaging formula is used to calculate image-object power relationship
L’=L+F
F=total power of the lens
Incident vergence (L)=no/l=ns/l=1.0/l (in air)
Emergent vergence (L’)=ni/l’=ns/l’=1.0/l’(in air)
Where l=object distance and l’=image distance

7. Object Image Relationships
The types of images and objects as well as sign convention are the same as for single refracting surfaces
object space
Image space
VIRTUAL OBJECTS
REAL IMAGES
REAL OBJECTS
VIRTUAL IMAGES
negative
positive

8. Problem
Virtual image is formed 25cm from a thin lens. If the object is real and positioned 50 cm from the lens, what is the lens power?
L’=L+F

9. Image-Object Relationships Focal Points
The primary and secondary focal points are calculated the same was as that for single curved surfaces. Assume the surrounding media is air (n=1)
F=-n/f=n’/f’ becomes F=-1.0/f=1.0/f’
The equation shows that for thin lenses f=f’, but they are opposite signs

10. Focal Points Recall that an infinite axial object forms an image at f’
Recall that an object placed at f, forms an image at infinity

11. Secondary focal point – convex surface
Object at infinity F’
f’ secondary focal length (+)
Rays converge towards secondary focal point

12. Secondary focal point –concave surface
Rays diverge as if they came from secondary focal point n n’
Secondary focal point F’
Object at infinity
f’ secondary focal length (-)

13. Primary focal point
The object position that yields the image at infinity
Emergent vergence (L’) is zero

14. Primary focal point- positive surface
F’ (infinity)
f (primary focal length)
f’ secondary focal length

15. Primary focal point – negative surface
Infinite image rays c F’ F
f primary focal length
f’’ secondary focal length

16. Problem
What are the primary and secondary focal lengths for a lens (n=1.49) with a power of -12D in air?
F=-n/f F=n’/f’

17. Image-Object Relationships Size and Orientation
This is LATERAL MAGNIFICATION and the ratio is image size/object size
- invereted/+erect
These equations are the basis for the lensometer
LM=h’/h=nl’/n’l=nsl’/nsl=l’/l
LM=-f/x=-x’/f’ (x= extrafocal dist)
Where x=dist from primary focal point to object and x’=dist from seconary focal point to image
Just as for single refracting surfaces, set up similar triangles!!!!!!!!!!!!!!!!!!!!!!

18. Lateral Magnification xx’=ff’ xx’=-f’f’ xx’=-(f)2h F c c h’ l l’ x’ x f f’

19. Problem LM
A real image moves to 5cm away from a lens when an object is moved from infinity to a position 40cm in front of the lens. What is the power of the lens?
xx’=-(f)2

20. Distant Object Size tanw=h’/f=-h’/f’ h’=-f’tanw
When an object is at an infinite distance, the LM cannot be determined. To solve for the object size use the chief ray
tanw=h’/f=-h’/f’
h’=-f’tanw F’ h’ h’ F f f’

21. Who cares?
The angular subtense of an object as it falls on the retina is used in vision to describe the size of a distant object.
A 20/60 letter on an eye chart subtends a 15 minute arc at 20 feet (1 degree= 60 minutes).

22. Prismatic Effect of Thin Lenses
The amount of bending after refraction is a function of the distance from the axis
Closer to the axis bends less
This is considered the prismatic effect of a lens
The change in direction is the deviation
Unlike a prism which has ONE deviation for any incident ray, a lens has an infinite number of deviations

23. Prismatic Effect of Thin Lensesd1 d2

24. Prismatic Effect of Thin Lenses
THERE IS NO PRISMATIC EFFECT AT THE OC OF A LENS
However, if the visual axis is not aligjed with the OC there is prism

25. Prismatic Effect of Thin Lenses
The image always shifts
Towards the APEX.
Positive lenses displace
Images opposite the direction
Of decentration
                        

26. Prismatic Effect of Thin Lenses
Lens decentered downward = base up. In general, negative lenses displace images
In the SAME direction as decentration.

27. Prismatic Effects
The magnitude of prismatic deviation in prism diopters is expressed in terms of displacement (cm) and the secondary focal length (m)
d=ycm/f’m = ycmFD

28. Prism Problem
Patient with PD of 60mm is given a frame with a 70mm PD. If the pt’s Rx is -3.00D OU, what is the direction and amount of induced prism?

29. Effective Power
Vergence (power) required for a lens at a new position to have the same effect on the incident rays.
Becomes important if the distance between a lens and an image plane (retina) is changed.
MOVING A LENS AWAY FROM THE IMAGE PLANE INCREASES POSITIVE POWER (DECREASES NEG. POWER)

30. Effective Power Fx=1/f’x=1/f’-d f’x Fx=F/1-dF p1 p2 screen
This is the situation when
You move a lens closer
(i.e. glasses going to contact
Lenses) F’
F’d
Fx=1/f’x=1/f’-d
Fx=F/1-dF
f’x d d f’

31. Effective Power p1 p2 When the lens is moved AWAY, then less power
Is required to put the image
In the same place
CLS to glasses
OR need more bifocal power F’ f’
If lens is moved to the right
d is positive, if lens is
Moved right to left, d is neg d d
f’x

32. Which soldier is taller?                                                                                                              

34. Is it moving and shimmering. Buy a poster
Is it moving and shimmering?                                                                                                    Buy a poster! Look at this illusion for a while and it will appear to be shimmering and moving. Also: Follow the outermost groove and watch it change from a groove to a hump as you go around the wheel.

35. Problem Sets
When rays from the sun pass through a convex lens, it makes a bright point image 0.7m behind the lens on the ground.
What is the focal length of the lens?
What is the nature of the image?
What is the magnification?
What is the power of the lens?

36. Problem Sets
A light bulb is placed 300 cm from a convex lens with a focal length of 50 cm.
Where is the image located?
What is the nature of the image?
What is the magnification of the image?

37. Problem Sets
A light bulb is placed 300 cm from a convex lens with a focal length of 500 cm.
Where is the image?
What is the nature of the image?
What is the magnification of the image?

38. Problem Sets
A slide is placed 50mm from a projector lens and no image is formed. Why?
An object of height 7cm is placed 25 cm in front of a thin converging lens with a focal length of 35 cm. What is the height, location and nature of the image?

39. Problem Sets
Now the object is moved to 90 cm. What is the new image distance, height, and nature of the image?

40. Problem Sets
A patient comes in having trouble with their new glasses which you prescribed. Their acuity is 20/20 in each eye and you determine that the refraction (-5.50 OD and X090 OS) is accurate. However, the patient reports that they glasses make them uncomfortable. You determine that the lenses have not been centered properly. They are decentered 2mm out on the OD and 2mm up on the OS. (how would you do that??). What is the induced prismatic effect?

41. Problem Sets
A patient has a 10D exophoria at near. The patient needs a D reading add. What amount of prism would you prescribe? How much decentration needs to be added? In what direction is the base of the prism?

42. Problem Sets
A patient with ARMD is having trouble reading. You determine that she needs a add on top of her distance Rx of OU to see the newspaper. How far away does she need to hold the paper to see it clearly? What will be the magnification of an object 10 cm tall held 5 cm from the lens?

43. Problem Sets
An object 0.08 m high is placed 0.2m from a (+) lens. If the distance of the image from the lens is .40m, what is the height of the image?
Diverging lenses form what kind of images?

44. Problem Sets
An object is placed 0.2m from a lens with a focal length of 1.0m. How far from the lens will the image be formed?