Understanding Transverse and Angular Magnification in Optics, Study notes of Optics

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Angular Magnification

Basic Optics , Chapter 22

 But first, let’s recall some of the facts about

transverse magnification…

Transverse Magnification

Transverse Magnification

But what about objects and images located at

infinity?

Image height Object height Image distance (v) Object distance (u) Transverse mag = =

Transverse Magnification

But what about objects and images located at

infinity?

Image height Object height Image distance (v) Object distance (u) Transverse mag = = Likewise, if the image is at infinity, then the transverse mag is infinitely large. (Huh?)

Transverse Magnification

But what about objects and images located at

infinity?

So, if the object is at infinity, then the transverse mag is undefined mathematically, approaching zero. (Huh?)

 In addition, consider the optics of an

afocal system (e.g., a telescope)

Parallel rays from an object at infinity Parallel rays to an image at infinity Astronomical (Keplerian) telescope Low plus lens High plus lens Parallel rays from an object at infinity Parallel rays to an image at infinity Low plus lens High minus lens Galilean (terrestrial) telescope Transverse Magnification

 In addition, consider the optics of an

afocal system (e.g., a telescope)

So, for telescopes, the transverse

magnification would seem to be:

Image distance (v) Object distance (u) = ∞/∞ = 1.

In other words, no

magnification at all!

Parallel rays from an object at infinity Parallel rays to an image at infinity Astronomical (Keplerian) telescope Low plus lens High plus lens Parallel rays from an object at infinity Parallel rays to an image at infinity Low plus lens High minus lens Galilean (terrestrial) telescope Transverse Magnification

 In addition, consider the optics of an

afocal system (e.g., a telescope)

So, for telescopes, the transverse

magnification would seem to be:

Image distance (v) Object distance (u) = ∞/∞ = 1. Parallel rays from an object at infinity Parallel rays to an image at infinity Astronomical (Keplerian) telescope Low plus lens High plus lens Parallel rays from an object at infinity Parallel rays to an image at infinity Low plus lens High minus lens Galilean (terrestrial) telescope Transverse Magnification What good is a telescope that doesn’t magnify?

 Clearly, transverse mag cannot meet all

our ‘magnification needs’

 We also need a measure that addresses the

apparent sizes of objects and images, not

just actual sizes

 That measure is angular magnification

 How big objects look , not how big they are

Angular Magnification

N

 Angular size is determined by the angular

extent of retina an image subtenses (θ)

θ Just as in any other optical system, the nodal point of the eye determines image location when ray tracing θ Angular Magnification

 Angular size is determined by the angular

extent of retina an image subtenses (θ)

θ N Consider this optical system…What would happen if we inserted a plus lens such that the object was located at its primary focal plane? Angular Magnification

 Angular size is determined by the angular

extent of retina an image subtenses (θ)

F 1 N N

Plus lens θ Primary focal plane of plus lens Consider this optical system…What would happen if we inserted a plus lens such that the object was located at its primary focal plane? Angular Magnification

 Angular size is determined by the angular

extent of retina an image subtenses (θ)

F 1 N N

θ

Consider this optical system…What would happen if we inserted a plus lens such that the object was located at its primary focal plane? All the rays will leave the lens parallel to the nodal ray, and… One of those rays will pass through the nodal point of the eye, Plus lens^ subtensing a new angular size Primary focal plane of plus lens Angular Magnification

 Angular size is determined by the angular

extent of retina an image subtenses (θ)

F 1 N N

θ

Virtual image at infinity Consider this optical system…What would happen if we inserted a plus lens such that the object was located at its primary focal plane? All the rays will leave the lens parallel to the nodal ray, and… We can trace this ray back and see where a magnified virtual image is located Plus lens Primary focal plane of plus lens One of those rays will pass through the nodal point of the eye, subtensing a new angular size It appears bigger! Angular Magnification