Page:MichelsonRefractometer1882.djvu/6

Substituting, we have $\varphi -{\tfrac {4\alpha _{2}t}{\lambda ^{3}\cos r}}=0$ or $n_{0}\cos i=n\cos r={\tfrac {2\alpha _{2}}{\lambda ^{2}\cos r}}={\tfrac {{\tfrac {2\alpha _{2}}{\lambda ^{2}}}+n\cos ^{2}r}{\cos i\cos r}}$, or finally,

$n_{0}={\frac {2\left(n-\alpha _{1}\right)+n\cos ^{2}r}{\cos i\cos r}}$

(8)

If the angle $i$ is small, the value of $n_{0}$ will vary very little with $i$, consequently there will be a large number of circles all nearly achromatised. Under favorable circumstances as many as one hundred rings have been counted, using an ordinary lamp, as source of light. The difference of path of the two pencils which produce these rings in white light may exceed a thousand wave lengths.