Understanding Magnifi cation
Organization for Standardization (ISO) , Geneva, Switzerland , 2017 ,
www.iso.org/standard/69042.html .
[20] CD Hendley , J Gen Physiol 31 ( 5 ) ( 1948 ) 433 – 57 . [21] H Strasburger et al. , J Vision 11 ( 5 ):13 ( 2011 ) 1 – 82 . [22] A Duane , Trans Am Ophthalmol Soc 20 ( 1 ) (1922 ) 132 – 57 .
Appendix Derivation of Equation 10:
For many cases, the viewing distance will be approximately the eye’s near point ( d vd ≈ d np ), so:
The diagram in Fgure A1 shows the same object being observed by a person from two different distances. One distance is the so-called “viewing distance” ( d vd ) and the other is the standard reference for the viewing distance based on the average near point ( d np ) of the human eye (the closest point on which the eye can focus), 250 mm [22]. The observed or perceived heights of the object are h vd at the viewing distance and h np at the eye’s near point. For rays of light coming from the top of the object and passing directly to the center of the eye’s lens in a straight line, the rays subtend an angle with respect to the horizontal of α vd for the object at the viewing distance position and α np at the eye’s near point. In Figure A2 , an equivalent result as for Figure A1 is shown using an imaginary lens system that produces a virtual image of the object. The object is placed at the eye’s near point ( d np ), and the virtual image of the object appears at the viewing distance position ( d vd ). Now Figure A2 of the diagram can be analyzed using basic geometrical optics in terms of magnification. The angular magnification, M ANG , and lateral magnification, M DIS (Equation 1), for Figure A2 are:
Figure A : (1) Diagram showing the same object observed by the unaided eye from two different distances, the “viewing distance” and average near point of the eye (250 mm). The viewing distance is represented by d vd and the eye’s near point by d np . The perceived heights of the object are h vd at the viewing distance and h np at the eye’s near point. Light rays coming from the top of the object in the two positions subtend an angle with respect to the horizontal of α vd (viewing distance position) and α np (eye’s near point). (2) Equivalent result as A1 using an imaginary lens system that produces a virtual image of the object. The object is placed at d np and the virtual image appears at d vd .
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Considering only the case of paraxial rays, then the angle α ≈ tanα . It can also be seen from Figure A2 that:
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Equating M ANG with the visual magnifi cation and knowing that d np is 250 mm and d vd the viewing distance , then:
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