In exercise 2.5 you are asked to make some replacements in your ray trace to generate a numerical trace. 

Copy and paste the output directly from Mathematica into the text box below when using the suggestion to see the output with //N. DO NOT MAKE ANY EDITS.

The results for 1.2 make sense because both rays just travel in straight lines

In exercise 1.2 the correct result for rfb should be

In Exercise 1.2 I obtained rfa={0.01+d, 0.}. Is this correct? Why or why not?

Do your eigenvectors obtained using Solve and those obtained using Eigenvectors agree? If not, is this a problem? Also if not, what (if any) is the relationship between them? 

What is the result of evaluating the following line of code (after completing exercises 4.1, 4.2 and 4.5)?

Simplify[M.evec1 == evals[[1]] evec1]&&Simplify[M.evec2 == evals[[2]] evec2]

In exercise 4.1 we ask that you characteristic equation and that requires the use of the identity matrix . How is a 2 x 2 identity matrix entered in Mathematica?

For this question select ALL answers that apply

The eigenvalues obtained using Solve and using Eigenvalues are the same

Exercise 3.7 asks you to summarise various key elements of ray tracing according to the things we have started to set up. 

In particular, please summarise here what the system matrix might look like for a ray moving a distance d1 encountering a thin lens and then moving a distance d2 and how we could combine (the matrices of) many lenses into a (system matrix for a) chain of lenses?

In exercise 3.3 you are asked to confirm that letting in the expression for Mthick reproduces the Mthin.  

Which of the following correctly checks for this (and returns True assuming Mthick and Mthin are correctly defined)?

Note there may be more than one correct answer, you only need to find one however.