- #1

- 116

- 3

## Homework Statement

I have to find the ray transfer matrix for a Plano convex lens, with a 5 cm radius and refraction index n=1.8.

I'm supposed to use the paraxial approximation.

Attached a homemade picture of the lens.

## Homework Equations

Refraction at a curved surface:

\begin{pmatrix}

1 & 0\\

\frac{n_1-n_2}{Rn_2} & \frac{n_1}{n_2}\\

\end{pmatrix}

Propagation matrix for the inside:

\begin{pmatrix}

1 & d\\

0 & 1\\

\end{pmatrix}

Refraction at a flat surface:

\begin{pmatrix}

1 & 0\\

0 & \frac{n_1}{n_2}\\

\end{pmatrix}

## The Attempt at a Solution

I would multiply the three matrices like this: [itex]

\begin{pmatrix}

1 & 0\\

0 & \frac{n_1}{n_2}\\

\end{pmatrix}

\begin{pmatrix}

1 & d\\

0 & 1\\

\end{pmatrix}

\begin{pmatrix}

1 & 0\\

\frac{n_1-n_2}{Rn_2} & \frac{n_1}{n_2}\\

\end{pmatrix}

[/itex]

What is d? Is it 5 cm because it's a half sphere and all rays travel 5 cm?

Kind regards Alex :)