Understanding Transverse Magnification in Optics, Schemes and Mind Maps of Geometry

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Transverse Magnification

Basic Optics , Chapter 20

 Let’s talk about transverse magnification

 Also known as lateral or linear magnification

 Transverse mag concerns the relative height

of objects and images in our ray tracings

Transverse Magnification

Transverse magnification is defined as:

Image height

Object height

F 1 F 2 Thin plus lens N Image height Object height Transverse Magnification

Transverse magnification is defined as:

Image height

Object height

F 1 F 2 Thin plus lens N Image height =? Object height =? OK, but how do we determine object and image heights when all we have (usually) is info re vergence? Transverse Magnification

F 1 F (^2) Thin plus lens N Here is a ray tracing from a previous chapter. Here it is with only the nodal ray and lens axis ray drawn. Transverse Magnification

F 1 F (^2) Thin plus lens N Here is a ray tracing from a previous chapter. Here it is with only the nodal ray and lens axis ray drawn. Think back to high-school geometry—what does the figure look like? Transverse Magnification

F 1 F (^2) Thin plus lens N u v O I θ θ Transverse Magnification

F 1 F (^2) Thin plus lens N u v O I Transverse magnification = I/O (by definition) θ θ Transverse Magnification

F 1 F (^2) Thin plus lens N u v O I Transverse magnification = I/O (by definition) By similar triangles: I/O = v/u Therefore, transverse magnification is determinable by simply taking a ratio of the image distance to the object distance θ θ Transverse Magnification

F 1 F (^2) Thin plus lens N u v O I Transverse magnification = I/O (by definition) By similar triangles: I/O = v/u θ θ

But we can make it more convenient still…

Transverse Magnification Therefore, transverse magnification is determinable by simply taking a ratio of the image distance to the object distance

…and the relationship

between vergence

(big U , big V )

and distance

(little u , little v )

 The Vergence Formula

u v

u = 1/U v^ = 1/V

Transverse Magnification

U + P = V

Vergence of incoming light Vergence contributed by the lens Vergence of light leaving lens

Recall the

Vergence

Formula …

F 1 F (^2) Thin plus lens N u v O I

U+P=V

θ θ

u = 1/U v^ = 1/V

SO , transverse magnification = I/O (by definition) AND , by similar triangles, I/O = v/u AND , by the Vergence Formula, v/u = = Transverse Magnification U V 1/V 1/U

F 1 F 2 Thin plus lens N Image height Object height u v

U+P=V

Transverse Magnification

So, in summary:

Transverse magnification is defined as: Image height Object height F 1 F 2 Thin plus lens N Image height Object height u v

U+P=V

Transverse Magnification