Light Displacement

A light ray is incident (with angle $\alpha$) on a rectangular block of transparent material with index of refraction n.

The angle $\beta$ of the transmitted beam can then be calculated with Snell's Law:

sin $\alpha$ = n sin $\beta$

On the other side of the block, another refraction occurs, and the outgoing ray again has the angle $\alpha$. So this is a displacement without a change in angle. As the drawing shows, it is displaced from the original ray by a distance $\delta$.

$\delta$ = a-b = d sin$\alpha$·{(1-sin²$\alpha$)^-1/2 - (n²-sin²$\alpha$)^-1/2}

In dealing with systems of lenses, one has the effect of refraction as well as this displacement effect. Usually, the diffraction effect dominates, however, and one neglects the displacement: This is the thin-lens approximation.

Note that the size of the displacement depends on the angle of incidence of the light. (This is the basis of a device called an optical micrometer, used for measuring very small displacements far away from the observer.)