Magnification Amy Nau, O.D. http://www.purdue.edu/hr/images/magnifyingGlass.jpg

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

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

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) http://www.medrounds.org/optics-review/uploaded_images/Figure34-745600.jpg

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

Linear/Transverse Magnification Ratio of image vergence to object vergence L’/L Ratio of image size to object size= I/O http://www.medrounds.org/optics-review/2006/05/27.html Linear/Transverse Magnification

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

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

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

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 +24.00D 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= +24.00D, M e = dF = 0.50(24) = 12X This indicates that closer working distances result in less effective magnification. Apparent Magnification

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

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

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

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

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

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

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

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

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)) (1/1-0.015)(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

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

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

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

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

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. http://webvision.med.utah.edu/imageswv/fovea-periphery.jpg Cortical Magnification