II.G-1
II. Light is a Ray (Geometrical Optics)
II.G. Ray Tracing Through More Complex Optical Systems
Using what we have learned thus far, we now ought to be able to trace rays that travel paraxially (close to the optical axis) from the source points of an initial object to the corresponding points of a final image through arbitrary combinations of thin lenses and reflecting and refracting interfaces.
Just remember to treat one element (i.e., lens or interface) at a time, following the path that light actually takes as it travels through the system to determine the order of the elements. At each element, the object is the image from the previous element, and the image becomes the object for the following element (except of course for the first and last elements).
Consider the following example. The object and image for the ith element are labeled Oi and Ii, respectively.
a a
O1 I1
O2 I2
O3
L1 L2 S5
S3
I4
O5 I3
O4
I5 Image + Thin Lens
n
Mirror Thick Lens
Object – Thin Lens
S4
In the diagram we demonstrate how all of the objects and images can be constructed using ray tracing alone (with 2 rays per element). But notice that we could have constructed these equally well using our formulas for the location and magnification of an image at a particular element. That is, we could have used the following:
at element L1: 1 1 1
1 1 1
1 1
s s f m s1
+ s
′ = ; = − ′;
at element L2: 1 1 1
2 2 2
2 2
s s f m s2
+ s
′ = ; = − ′ ;
at element S3: 1 1 1
3 3 3
3 3
s 3
n s
n
R m
n s + s
′ = − = − ′
; ;
at element S4: n
s s
n
R s s
n m n s
4 4 4 s
4 4
4 4
4
1 1
0 1 1
+ ′ = −
→ ∞ = ⇒ ′ = − ; = − ′ = + ;
at element S5: 1 1 2
5 5 5
5 5
s s R m s5
+ s
′ = − ; = − ′ .
Whether you trace rays or simply use the formulas to follow the progression of images through a complex optical system is a matter of taste. However, your safest bet is to use one method to check the other: use the formulas to obtain quantitative results, but do some ray tracing to make sure your results are physically meaningful!
