BRIGHAM YOUNG UNIVERSITY
 Search BYU
 Contact   |   Help

[expand all...]
[COLLAPSE ALL...]

# Table of ABCD Matrices for simple optical components

Element Matrix Remarks
Propagation in free space or in a medium of constant refractive index d = distance
Refaction at a flat interface n1 = initial refractive index
n2 = final refractive index
Refaction at a curved interface R = radius of curvature, R > for convex (centre of curvature after interface)
n1 = initial refractive index
n2 = final refractive index
Reflection from a flat mirror Identity matrix
Reflection from a curved mirror R = radius of curvature, R > 0 for convex
Thin lens f = focal length of lens where f > 0 for convex/positive (converging) lens. Valid if and only if the focal length is much greater than the thickness of the lens

# ABCD Matrix Example

## Note: Each element in the numbered list corresponds with a 2 by 2 transfer matrix in the expression below (they are numbered respectively)

#### ☆ ☆ ☆ One of the properties of ABCD matrices that makes them extremely useful is that a system of several optical elements can be described by a single ABCD matrix. This ABCD matrix is the product of the ABCD matrices of each of the optical elements in the system. ☆ ☆ ☆

1. Transfer matrix of the medium between points 1 and 2 (with constant index of refraction n1)
2. Transfer matrix of the flat interface at point 2
3. Transfer matrix of the medium between points 2 and 3 (with constant index of refraction n2)
4. Transfer matrix of the flat interface at point 3
5. Transfer matrix of the medium between points 3 and 4 (with constant index of refraction n1)
6. Transfer matrix of the thin lens with focal length f and index of refraction n3
7. Transfer matrix of the medium between points 4 and 5 (with constant index of refraction n1)
8. Transfer matrix of the curved interface at point 5
9. Transfer matrix of the medium between points 5 and 6 (with constant index of refraction n4)
10. Transfer matrix of the flat interface at point 6
11. Transfer matrix of the medium between points 6 and 7 (with constant index of refraction n1)
12. Transfer matrix of the flat mirror at point 7
13. Transfer matrix of the medium between points 7 and 8 (with constant index of refraction n1)

Maintained by ECEn IMMERSE Web Team.