1. Magnification Amy Nau, O.D.

2. Types of Magnification
Angular
Apparent (Conventional/ Effective/Loupe)
Axial/longitudinal
Combined/total
Cortical
Relative distance
Electronic/transverse
Iso-accommodative
Lateral/linear
Spectacle
Relative spectacle
Relative size
Shape
Power
Types of Magnification

3. Angular Magnification
Ratio of object angle to image angle
This is why objects appear larger as they move closer to the eye
Angular Magnification

4. Angular Magnification
M = tan α′/tan α
M=angle image device /angle original object
This optical system produces a virtual image smaller than the original object but much closer to the eye. The image has a larger angular subtense than the original object; therefore, the objects appear larger when seen through this optical system even though the virtual image is smaller than the object.
The object is not changed in position or size, but has a lens between the object and the eye which makes it appear larger (magnifying glass, hand magnifier, telescopes)

5. Angular Magnification basic concepts
Mag 0-1 means image is smaller than object
Mag >1 means image is larger than object
Mag=1 same size (no mag)
If the image is farther from the lens than the object it will be larger (magnified) and vice versa
Image is erect if on same side of lens as object (like a mirror)- virtual image
+ upright/ - inverted
Angular Magnification basic concepts

6. Linear/Transverse Magnification
Ratio of image vergence to object vergence L’/L
Ratio of image size to object size= I/O
Linear/Transverse Magnification

7. Problem image size/object size or image dist/obj dist
Calculate transverse mag for the following
F=+8
Object distance 100 cm
image distance is 1/8=0.14m
So, 0.14/1=0.14 (minimized)
Problem image size/object size or image dist/obj dist

8. Axial (Longitudinal) Magnification
M= M1X M2
Axial magnification is used when talking about 3D objects
Axial magnification is the distance between the two image planes divided by the distance between the two object planes (extreme anterior and posterior points on the object with their conjugate image points)
Axial (Longitudinal) Magnification

9. Axial (Longitudinal) Magnification
Take incoming vergence front and back of object and calculate the emergent vergence front and back then get the ratio.
Axial (Longitudinal) Magnification

10. Apparent Magnification
Syn: Conventional/Effective/Loupe/Relative
M e = dF
Where d = distance in meters to the object (image is formed at infinity)
Question: A D lens is used as a hand held magnifier with the patient viewing an object that is 50cm from the eye and at the focal point of the lens. How much larger do things appear to the patient?
Answer: d = 0.50m, F= D, M e = dF = 0.50(24) = 12X
This indicates that closer working distances result in less effective magnification.
Apparent Magnification

11. Conventional Magnification
Conventional Magnification = Mc = dF + 1
The underlying assumption in this equation is that the patient is “supplying” one unit (1X) of magnification otherwise it is the same as apparent magnification
Used for low vision
Conventional Magnification

12. Total (Combined) Magnification
Generally used for microscopes, but basically you multiply the individual lens mags together
MT= M1 X M2 X M3…..
So you have a 15 x eyepiece and a 10x objective for total mag of 150x.
Total (Combined) Magnification

13. Electronic Magnification
CCTV, computers, video, Brainport
It is equal to the ratio of the size of the image on the screen to the size of the original object being viewed.
Example: an object 2cm in height measures 6 cm on the screen, the magnification is 6/2 = 3✕.
Electronic Magnification

14. relative distance magnification
The magnification that results from decreasing the distance between an object and the eye. It is expressed as
Md = x/x′
where x and x′ are the initial distance and the new distance, respectively.
Example: if the viewing distance is decreased from 60 cm to 20 cm, Md = 60/20 = 3✕.
relative distance magnification

15. Iso- Accommodative Magnification
The magnification of a lens (or lens system) when the distance of the image from the eye (or spectacle plane) formed by a magnifier is equal to the distance of the object from the eye viewed without the magnifier. Thus the same amount of accommodation (or near addition) is required with or without the magnifier. It is equal to
M = 1 + (F/D)
where F is the power of the magnifier (assumed to be so close to the eye as to ignore the distance separating them) and D the object vergence.
Iso- Accommodative Magnification

16. Spectacle Magnfication
How much glasses magnify or minify the retinal image size
It is >1 in the hyperopic eye, <1 in myopia.
With a contact lens, this magnification is 1 whatever the refractive error.
Depends on
Lens thickness
Material (index)
Vertex distance
Base curve of the front of the lens
Spectacle Magnfication

17. Spectacle Magnification
SM=(shape factor) x (power factor)
Shape factor relates to base curve and lens thickness
Power factor relates to overall lens power and vertex distance
SM = (1/1-(t/n)D1) x (1/1-hD)
Where: n=index of refraction; D1=front surface power (base curve); D = total lens power; h= vertex dist +3mm (b/c calculated at entrance pupil not corneal plane)
Spectacle Magnification

18. Spectacle Magnification
In the case of aniseikonia, eikonic lenses can be prescribed which try to reduce magnification effects by manipulating BC
Thickness
Vertex distance
Can be cosmetically unacceptable
Spectacle Magnification

19. What is the SM for each lens, the difference in mag percent and how can you minimize the difference?
OD: +1.50; BC +6.25; t=3mm
OS: +4.50; BC +9.25; t=5mm
Vertex 12mm
N=1.498
SM OD = (1/1-(0.003/1.498)(6.25)) (1/1-(0.015)(1.50)=1.036
%SM= (SM-1)(100)= 3.6%
SM OS: (1/1-(0.005/1.498)(9.25)) (1/ )(4.50)=1.107
% SM = 10.7%
Difference in SM is thus 7.1%
You can try to manipulate BC, t, vertex, index. Need to check each one to see which may work

20. Spectacle Magnification
Rare to change all 3 variables
Choose small, round frame fitting close to face
Aspheric lenses
Acceptability of poor cosmesis usually related to functional outcome.
Spectacle Magnification

21. Relative Spectacle Magnification
The ratio of the retinal image size in the corrected ametropic eye to that in a standard emmetropic eye.
Relative Spectacle Magnification

22. Relative Size Magnfication
The magnification which results from increasing the actual size of an object viewed. Examples: a larger TV screen; a larger print book than one used previously. It is expressed as
Ms = h2/h1
where h2 and h1 are the sizes of the enlarged object and the initial object, respectively.
Syn. size magnification; relative size enlargement.
Relative Size Magnfication

23. Lateral Magnification
Magnification of a lens or of an optical system, expressed as the ratio of the size of the image h′ to the size of the object h. It is usually denoted by
M = h′/h = l′/l = L/L′
where l′ and l are the distances of the image and object, respectively from the principal plane of the lens (or lens system) and L and L′ the object and image vergences
Lateral Magnification

24. Cortical Magnification
Term referring to the fact that the amount of cortical area devoted to processing visual information from the central area of the retina far exceeds the amount devoted to the peripheral retina.
It is estimated that about 25% of the cells in the visual cortex are devoted to processing the central 2.5º of the visual field.
Cortical Magnification