Axial Magnification Basic Optics Chapter 21 2 Axial
Axial Magnification Basic Optics, Chapter 21
2 Axial Magnification l l l 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
3 Axial Magnification Note the addition of an axial component to the object (and therefore image) Thin plus lens Image Object F 1 N F 2
4 Axial Magnification You will recall that transverse mag is defined as: Image height Object height Thin plus lens Object height Image Object F 1 N F 2 Image height
5 Axial Magnification You will recall that transverse mag is defined as: Image height Object height Likewise, axial magnification is defined as: Image width Object width Thin plus lens Object width Object height Image Object F 1 N F 2 Image height Image width
6 Axial Magnification l Axial magnification can be approximated by the square of the transverse magnification Axial mag ≈ (Transverse mag)2
7 Axial Magnification Axial Transverse magnification is defined as: Axial Image height Object height 2 Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) 2 (By similar triangles) Image distance (v) Object distance (u) 2
8 Axial Magnification Axial Transverse magnification is defined as: Axial Image height Object height 2 Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) (By similar triangles) 2 Image distance (v) Object distance (u) Thin plus lens 2 U+P=V Object height F 1 u N F 2 v Image height
9 Axial Magnification Axial Transverse magnification is defined as: Axial Image height Object height 2 Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) (By similar triangles) 2 Image distance (v) Object distance (u) Thin plus lens 2 U+P=V Object height If u = -100 cm, and P = +3, then v = ? F 1 u N F 2 v Image height
10 Axial Magnification Axial Transverse magnification is defined as: Axial Image height Object height 2 Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) (By similar triangles) 2 Image distance (v) Object distance (u) Thin plus lens 2 U+P=V Object height If u = -100 cm, and P = +3, then v = 50 cm F 1 u N F 2 v Image height
11 Axial Magnification Axial Transverse magnification is defined as: Axial Image height Object height 2 Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) (By similar triangles) 2 Thin plus lens U+P=V Object height If u = -100 cm, and P = +3, then v = 50 cm Transverse mag = v/u = 50/-100 = ? Image distance (v) Object distance (u) 2 F 1 u N F 2 v Image height
12 Axial Magnification Axial Transverse magnification is defined as: Axial Image height Object height 2 Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) (By similar triangles) 2 Thin plus lens U+P=V Object height If u = -100 cm, and P = +3, then v = 50 cm Transverse mag = v/u = 50/-100 = -. 5 Image distance (v) Object distance (u) 2 F 1 u N F 2 v Image height
13 Axial Magnification Axial Transverse magnification is defined as: Axial Image height Object height 2 Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) (By similar triangles) 2 Thin plus lens U+P=V If u = -100 cm, and P = +3, then v = 50 cm F 1 u N F 2 Image height v inverted Object height Transverse mag = v/u = 50/-100 = -. 5 Image distance (v) Object distance (u) 2 (The. 5 tells us the image is ½ the size of the object; the minus sign indicates the image is inv erted )
14 Axial Magnification Axial Transverse magnification is defined as: Axial 2 Image height Object height Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) (By similar triangles) 2 Image distance (v) Object distance (u) Thin plus lens 2 U+P=V Object height If u = -100 cm, and P = +3, then v = 50 cm F 1 Transverse mag = v/u = 50/-100 = -. 5 u 10 cm If our arrow has a 10 cm ‘nose, ’ how big will the image nose be? N F 2 Image height v ?
15 Axial Magnification Axial Transverse magnification is defined as: Axial 2 Image height Object height Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) (By similar triangles) 2 Thin plus lens U+P=V Object height If u = -100 cm, and P = +3, then v = 50 cm F 1 Transverse mag = v/u = 50/-100 = -. 5 Axial mag = (v/u)2 = -. 52 =. 25 Image distance (v) Object distance (u) 2 u 10 cm If our arrow has a 10 cm ‘nose, ’ how big will the image nose be? N F 2 Image height v ?
16 Axial Magnification Axial Transverse magnification is defined as: Axial Image height Object height 2 Transverse magnification is equal to: (By the Vergence Law) Vergence of incoming light (U) Vergence of light leaving lens (V) (By similar triangles) 2 Thin plus lens U+P=V Object height If u = -100 cm, and P = +3, then v = 50 cm F 1 Transverse mag = v/u = 50/-100 = -. 5 Axial mag = (v/u)2 = -. 52 =. 25 Image distance (v) Object distance (u) 2 u 10 cm N F 2 Image height v 2. 5 cm If our arrow has a 10 cm ‘nose, ’ how big will the image nose be? . 25 x 10 cm = 2. 5 cm (approx)
17 Axial Magnification l l 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
18 Axial Magnification l l 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)
19 Axial Magnification l l 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) Image lesion height = 60 20 D Mathematically convenient PD (it’s a little low) = 3 x Typical condensing lens power
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