Angular Separation of the Visible Spectrum
A right angle prism (quartz;
i.e., silica) has equal legs. If white light is incident at 25o from the
surface as shown, what is the angular separation between the limits of
the visible spectrum?
The wavelengths are 400 to 700
nm. From page 1034, Figure 35.15, the indices of refraction are 1.471 and
1.459, respectively.
Using a numbering system for
the angles in order from the right, and using n for the index of refraction
of the glass (it varies, depending on the wavelength!):
Using Snell's law at the second
interface,
This is ideal for a spreadsheet
calculation:
n
|
angle 3
|
angle 4
|
1.471
|
6.9669
|
10.278
|
1.459
|
6.5974
|
9.6499
|
The difference between the two
"angles 4" is 0.628. This is the angular separation.