Axial Magnification Basic Optics, Chapter 21

Axial Magnification We saw in Chapter 20 that transverse mag addresses the relative heights of an image and object But what about changes in the ‘fore and aft’ (i.e., along the lens axis) relative sizes? This is captured by axial magnification

Axial Magnification Note the addition of an axial component to the object (and therefore image) Thin plus lens Image Object F1 N F2

You will recall that transverse mag is defined as: Axial Magnification Image height Object height You will recall that transverse mag is defined as: Thin plus lens Object height Image Object F1 N F2 Image height

You will recall that transverse mag is defined as: Axial Magnification Image height Object height You will recall that transverse mag is defined as: Image width Object width Likewise, axial magnification is defined as: Object width Thin plus lens Object height Image Object F1 N F2 Image height Image width

Axial Magnification Axial mag ≈ (Transverse mag)2 Axial magnification can be approximated by the square of the transverse magnification Axial mag ≈ (Transverse mag)2

Axial Magnification 2 Axial Axial 2 2 Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u)

Axial Magnification U+P=V 2 Axial Axial 2 2 u v Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u) Thin plus lens U+P=V Object height F1 N F2 Image height u v

Axial Magnification U+P=V 2 Axial Axial 2 2 If u = -100cm, and Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u) Thin plus lens U+P=V Object height If u = -100cm, and P = +3, then v = ? F1 N F2 Image height u v

Axial Magnification U+P=V 2 Axial Axial 2 2 If u = -100cm, and Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u) Thin plus lens U+P=V Object height If u = -100cm, and P = +3, then v = 50cm F1 N F2 Image height u v

Axial Magnification U+P=V 2 Axial Axial 2 2 If u = -100cm, and Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u) Thin plus lens U+P=V Object height If u = -100cm, and P = +3, then v = 50cm F1 N F2 Image height Transverse mag = v/u = 50/-100 = ? u v

Axial Magnification U+P=V 2 Axial Axial 2 2 If u = -100cm, and Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u) Thin plus lens U+P=V Object height If u = -100cm, and P = +3, then v = 50cm F1 N F2 Image height Transverse mag = v/u = 50/-100 = -.5 u v

Axial Magnification U+P=V 2 Axial Axial 2 2 If u = -100cm, and Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u) Thin plus lens U+P=V Object height If u = -100cm, and P = +3, then v = 50cm F1 N F2 Image height Transverse mag = v/u = 50/-100 = -.5 u v (The .5 tells us the image is ½ the size of the object; the minus sign indicates the image is inv erted ) inverted

Axial Magnification U+P=V 2 Axial Axial 2 2 If u = -100cm, and Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u) Thin plus lens U+P=V Object height If u = -100cm, and P = +3, then v = 50cm F1 N F2 Image height Transverse mag = v/u = 50/-100 = -.5 u v ? 10cm If our arrow has a 10cm ‘nose,’ how big will the image nose be?

Axial Magnification U+P=V 2 Axial Axial 2 2 If u = -100cm, and Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u) Thin plus lens U+P=V Object height If u = -100cm, and P = +3, then v = 50cm F1 N F2 Image height Transverse mag = v/u = 50/-100 = -.5 u v Axial mag = (v/u)2 = -.52 = .25 ? 10cm If our arrow has a 10cm ‘nose,’ how big will the image nose be?

Axial Magnification U+P=V 2 Axial Axial 2 2 If u = -100cm, and Image height Object height Transverse magnification is defined as: Axial Transverse magnification is equal to: (By the Vergence Law) (By similar triangles) 2 2 Vergence of incoming light (U) Vergence of light leaving lens (V) Image distance (v) Object distance (u) Thin plus lens U+P=V Object height If u = -100cm, and P = +3, then v = 50cm F1 N F2 Image height Transverse mag = v/u = 50/-100 = -.5 u v Axial mag = (v/u)2 = -.52 = .25 10cm 2.5cm If our arrow has a 10cm ‘nose,’ how big will the image nose be? .25 x 10 cm = 2.5 cm (approx)

Axial Magnification Axial magnification is important in the context of indirect ophthalmoscopy The condensing lens power and the pupillary distance (PD) on the indirect ophthalmoscope determine the perceived height of elevated posterior pole lesions

Axial Magnification Axial magnification is important in the context of indirect ophthalmoscopy The condensing lens power and the pupillary distance (PD) on the indirect ophthalmoscope determine the perceived height of elevated posterior pole lesions Image lesion height = PD in millimeters Condensing lens power (D)

Mathematically convenient Axial Magnification Axial magnification is important in the context of indirect ophthalmoscopy The condensing lens power and the pupillary distance (PD) on the indirect ophthalmoscope determine the perceived height of elevated posterior pole lesions Image lesion height = PD in millimeters Condensing lens power (D) Mathematically convenient PD (it’s a little low) 60 Image lesion height = = 3x 20D Typical condensing lens power