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## Homework Statement

The problem is: The left end of a long glass rod 10.0 cm in diameter, with an index of refraction 1.5, is ground and polished to a convex hemispherical surface with a radius of 5.0cm. An object in the form of an arrow 2.00mm tall, at right angles to the axis of the rod, is located on the axis 25.0 cm to the left of the vertex of the convex surface. Find the position and height of the image of the arrow formed by paraxial rays incident on the convex surface.

From this I know that R= 5cm, do = 25cm, ho=.2cm, n1 = 1, n2 = 1.5

## Homework Equations

n1/n2

-(nlarge - nsmall)/n2R

## The Attempt at a Solution

(and what an attempt it is.)The teacher wants us to use ray matrices to figure out the answer. I figure there are 3 matrices that will need to be formed.

Here is what I have:

[tex]m1 = \left(\begin{array}{cc}

1 & 25 \\

0 & 1\\

\end{array}

\right)[/tex]

[tex]m2 = \left(\begin{array}{cc}

1 & 0 \\

-0.067 & .67\\

\end{array}

\right)[/tex]

[tex]m3 = \left(\begin{array}{cc}

1 & di \\

0 & 1\\

\end{array}

\right)[/tex]

When I multiply the 3 together I get my final result as:

[tex]mfinal = \left(\begin{array}{cc}

2.675 & 2.675di + 16.75 \\

-.067 & -.067di +.67\\

\end{array}

\right)[/tex]

For some reason I am not getting the right answers in my final matrix to lign up with the image matrix. Any help would be appreciated.

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