1. Axial Magnification
Basic Optics, Chapter 21

2. 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

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

4. 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

5. 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

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

7. 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)

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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?

15. 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?

16. 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? x 10 cm = 2.5 cm (approx)

17. 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

18. 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)

19. 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