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Mirrors are a key component of many optical devices. The matrix for the reflection at a spherical mirror was considered in the introductory chapter. We will now discuss reflectors more generally.
The matrix describing the reflection at a plane mirror can be obtained by taking the matrix for reflection at a spherical reflector and letting the radius of the spherical mirror tend to infinity. In this way, the unity matrix is obtained as A=[1 0 0 1 ]. The signs that appear in this matrix are surprising at first, and it is instructive to derive the matrix also in an alternative way. In Fig. 2.1, the reflection of a ray at a plane mirror, which is perpendicular to the optical axis, is depicted. In the matrix representation used here, we unfold the ray using the reference plane of the mirror as the plane of the coordinate break. Figure 2.2 shows the result of this "unfolding." It is this coordinate break that causes the positive signs in the matrix of the plane reflector.
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