Element 
Matrix 
Remarks 
Propagation in free space or in a medium of constant refractive index 

d = distance 
Refaction at a flat interface 

n_{1} = initial refractive index n_{2} = final refractive index 
Refaction at a curved interface 

R = radius of curvature, R > for convex (centre of curvature after interface)
n_{1} = initial refractive index n_{2} = 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 