Relationships derived from Snell's law
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Image position of a light ray incident on a material
The light rays before and after entering the material are shown in the figure below.
Here, dw, dθ1 , and dθ2 are small quantities.
The conditions shown in the figure can be expressed as follows:
Here,
Therefore,
Therefore,
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Image position when a parallel plate is placed perpendicular to the optical axis
Consider the following light beam that enters a plane-parallel plate and forms an image at the exit point. Calculate s in this case.
Here, dh, dθ 1 , and dθ 2 are small quantities.
The conditions shown in the figure can be expressed as follows:
Where:
Therefore,
Therefore,
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Image position when a parallel plate is placed at an angle to the optical axis
Consider the following light beam that is obliquely incident on a parallel plane plate and forms an image at the exit point. Calculate Δx and Δy in this case.
Here, dh, dθ 1 , and dθ 2 are small quantities.
The conditions shown in the figure can be expressed as follows:
Differentiate both sides of ③ to get
From ①, ②, ③', ④, and ⑤, eliminating s, xA, xB, dh, dθ1, and dθ2, we get
Here, from ① and ⑥,
Also, from ③,
Therefore, the solution we seek can be expressed as follows:
Furthermore, by applying ③ and eliminating θ2, we get
