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Lateral displacement of refraction

How to find and see the lateral displacement of light when entering a new material with different refractive index? Here you can see the answer. The segment between arrows is the lateral displacement. α is the refracted angle according to the refractive index. β is the remaining angle, which is the size the the angle turned between two materials. The longer dotted line ray is the original path without that material. The shorter dotted line segment is the horizontal segment which represents the width of the material. Update #1 (4/4/2015 06:12 UTC+0): Refractive index is changed to 2 decimal places. The lateral displacement display is changed to 5 decimal places.
The step is given.