\(\angle P=\cfrac{cf+cf' }{\lambda_i}{sin(\theta_i)}*\pi\)
where
\(cf'=\lambda _{ r }\left[ tan(\theta _{ r })-{ 2 }{ cosec(2\theta _{ r }) }+{ cosec(\theta _{ r }) } \right] \)
and
\(cf=\lambda _{ i }\left[ tan(\theta _{ i })-{ 2 }{ cosec(2\theta _{ i }) }+{ cosec(\theta _{ i }) } \right] \)
Specifically, if we consider,
\( \cfrac { \lambda _{ i } }{ \lambda _{ r } } =\cfrac { sin(\theta _{ i }) }{ sin(\theta _{ r }) } =1.5\)
\(\theta _{ r }=sin^{-1}\left(\cfrac { sin(\theta _{ i }) }{ 1.5 }\right)\)
and plot \(\angle P\) with respect to \(\theta_i\) only, we have,
When we zoomed in \(-\small{\cfrac{\pi}{2}}\le \theta_i\le\small{\cfrac{\pi}{2}}\),
\(cf'\) is sinusoidal. The phase different changes from zero up to \(\approx 1.25\pi\).
Being able to quantify phase here, allows for manipulating phase in optical signals easier.
By varying phase, it is possible to project a pseudo-3D image out from a flat screen.
