Supposing the ray to proceed both ways out of the prism at
and
the angle of incidence at
is less than that at
namely,
the latter being the exterior angle of the triangle
the former an interior and opposite angle.
Now the greater the angle of incidence, the greater is that of deviation, for if
be the angles of incidence and refraction,
is the deviation.
Then since
Now as
increases,
increases also, and the sine of
increases faster than that of the larger angle
so that the whole of the 2nd member of this equation increases; therefore
must increase also, to maintain the equality, and consequently
the deviation must increase.
In the above case then, the deviation at
being greater than that at
the inflexion of the ray is, on the whole, from the angle of the prism.
71. In making experiments with a prism through which a beam of light is made to pass in a plane perpendicular to its axis, it will be found, that if the prism be turned on its axis, the deviation of the emergent ray from the incident, will in some cases increase, in others diminish, so as to have a minimum value. Let us see to what case that value answers.
Adopting the same notation as before, we have
![{\displaystyle \delta =\phi +\psi -\iota ;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b47c5f886905fa61323202827b3ebf7b726ebe1b)
![{\displaystyle \sin \phi =m\sin \phi ';}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d250cded19d7e19e70ae0e2c96a5987c702b41c4)
![{\displaystyle \sin \psi =m\sin \psi ';}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d81ad80c162d0e1b98b88b20a6c5b31c30a7f68d)