So I've gotten through half of this very long problem involving thick lens matrices and using the calculated system matrix for image locations. I need help at part d!!!! I'm going mad with it.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]S = \begin{array}{cc}\frac{11}{8}&\frac{5}{2}\\\frac{3}{20}&1\end{array}[/tex] Athickglass lens (n=1.6) whose first surface has a radius of curvature of +5cm and a

thickness of 4cm and whose second surface is flat, is in air.

a) Starting with refraction and translation matrices, write down and simplify the system matrix for the lens

alone, taking the input and output planes to be at the start and end of the lens respectively. Please use the

"in class" method.

So I ended up with a system matrix with elements a11= 11/8 a12= 5/2 a21= 3/20 a22= 1. Calculations were S1=

r2 x t1 x r1. Looks good so far.

I did this correct I think, I'm trying to get my scanner to work now. b) Using the matrix elements from part a, locate all cardinal points and sketch them on a scale

diagram, showing and labeling all distances.

I got an answer of -60/11 cm, that's to the left of the right side of the lens. c) Using the object, image focal length equation (-f1/So + f2/Si = 1) locate the image of an object placed 30

cm in front of the lens. Be specific and give the location relative to the flat side of the lens.

I got a system matrix of elements a11= 11/8 + 6x/40, a12= 11s/8 + 6sx/40 + x + 5/2, a21= 6/40, a22= 1 + d) Now consider an object located at a distance s in front of the lens and its image, located at x

beyond the lens. Now write down and simplify the extended system matrix, taking the input plane to be at s

and the output plane to be at x. Keep s and x as variables in your answer.

6s/40. I took the original three refraction and transfer matrices and added two more transfer matrices, one

for s and x. Calculations were S1= t3 x r2 x t2 x r1 x t1.

I have no idea how to do this. I figured out the focal lengths, and they came out to be the same as in part e) Using the matrix elements from your matrix in part d), find the image location and the

magnification if your object is placed at s= 30cm. Does your result match your calculation in part c? I hope

so!

B, but the matrix in part D has the first two elements with respect to x when s= 30cm. Do I use matrix

algebra to solve for x? What about magnification. I think I missed a lecture.

The rest of the problem:

It acts like a thin lens doesn't it? p and q will be zero, focal points will be on their respective input and f) What information can you get from setting matrix elements A and D equal to zero in your matrix from

part d)? Try it. Do your results agree with your diagram from part b)? Explain.

output planes. That's all I have figured out.

Simple; you multiply the system matrix by an object matrix o11, o21 to solve an image matrix i11, i21 with g) For this situation in part e), trace a ray (mathematically) emanating from a point on the object

0.75cm above the optical axis at an angle of (2/3) radians too determine the height and angle of the ray at

the image location.

height and angle as elements.

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# Homework Help: Optics Matrix Methods

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