Have I set up these simple Ray Transfer Matrix problems the correct way? (error)

[Markus86]

I am currently getting used to the Ray Transfer Matrix for paraxial rays, and I was wondering if I have done the correct work on these problems, which I have kept as simple as possible:

http://www.image-share.com/upload/3903/99.jpg

http://www.image-share.com/upload/3903/100.jpg

In the first picture I have checked if I get a ray that ends up 3 unit lengths about the bottom of the rectangle (which has the same refractive index as air) and has the same angle as the original ray;
it does have the same angle, but it only has almost the same length, even though my graphical prediction clearly indicates that it should have a final height of 3.
What's going on there?

In the second picture I have tried out a very simple refraction scenario, where a ray in air enters a piece of glass with refractive index 1.5;
I get the expected height (which is unchanged), but the angle is very slightly different from the expected angle.

I have made sure to use exact values as far as possible, so this has nothing to do with error propagation.

Should I perhaps expect these errors, since I am dealing with paraxial rays?
I am very new to all of this.

[jayrandom]

Originally Posted by Markus86

I am currently getting used to the Ray Transfer Matrix for paraxial rays, and I was wondering if I have done the correct work on these problems, which I have kept as simple as possible:

http://www.image-share.com/upload/3903/99.jpg

http://www.image-share.com/upload/3903/100.jpg

In the first picture I have checked if I get a ray that ends up 3 unit lengths about the bottom of the rectangle (which has the same refractive index as air) and has the same angle as the original ray;
it does have the same angle, but it only has almost the same length, even though my graphical prediction clearly indicates that it should have a final height of 3.
What's going on there?

In the second picture I have tried out a very simple refraction scenario, where a ray in air enters a piece of glass with refractive index 1.5;
I get the expected height (which is unchanged), but the angle is very slightly different from the expected angle.

I have made sure to use exact values as far as possible, so this has nothing to do with error propagation.

Should I perhaps expect these errors, since I am dealing with paraxial rays?
I am very new to all of this.

The small errors you’re seeing are from the paraxial approximation, which makes the approximation sin(theta) = theta and cos(theta) = 1

In example 1, for instance, the exact expression is d tan(theta) not d * theta. As you can the difference is small but not zero.