Not Quite Photon Mass

Consider the force on the dipole in circular motion,

$F={m}_{p}\cfrac{c^2}{r}={m}_{p}r.\omega^2={m}_{p}r.(2\pi .f)^2$

this is also the force driving a photon to light speed $c$ and the drag force such that the photon is at terminal velocity.  For a given medium $F$ is a constant.

 $\omega^{ 2 }=\cfrac { F }{ { m }_{ p } } \cfrac { 1 }{ r }$

 $\log(\omega)=\cfrac { 1 }{ 2 } \log(\cfrac { F }{ { m }_{ p } } )-\cfrac { 1 }{ 2 } \log(r)$

A plot of $log(\omega)$ vs $\log(r)$ can then provide a value for $\cfrac{F}{{m}_{p}}$

Since $F$ is characteristic of a particular medium, we generate a number of y-intercepts ${y}_{i}$for different mediums ${n}_{i}$.  We know that,

$F\propto {c}^{2}$ and in a medium of refractive index $n_i$, ${v}^2_{s}=\cfrac{{c}^{2}}{n^2_i}$

as such,

${F}_{i}=\cfrac{F_o}{{n}_{i}}$,  where $F_o$ is the driving force in vacuum.

${y}_{i} =\cfrac { 1 }{ 2 } \log(\cfrac { F_o }{ { m }_{ p } } ) - \cfrac { 1 }{ 2 }log{({n}_{i})}$

A plot of ${y}_{i}$ vs $log{({n}_{i})}$ will provide a value for  $\cfrac{F_o}{{m}_{p}}$.

From the Post "Wave Front and Wave Back" , after total internal reflection,

${r}_{c2} = \cfrac{{r}_{c1}}{cos(\theta)}.\sqrt{(\cfrac{{n}_{1}}{{n}_{2}})^2.sin^2{(\theta)}-1}$

${r}_{c2} = {r}_{c1}$ when

$cos{(\theta)}=((\cfrac{n_1}{n_2})^2-1)^\cfrac{1}{2} ({(\cfrac{n_1} {n_2})^2+1})^{-\cfrac{1}{2}}$

A diagram of total internal reflection at this angle is shown,

As the ray enters the second medium ${n}_{2}$ photons speed up tracing a longer path.  The intrusion into ${n}_{2}$ is given by $\cfrac{2r.cos{(\theta)}}{tan{(\theta)}}$ which can be measured.  Given different frequency $f$, $r$ is different at the same angle of incident $\theta$.  Hopefully the first plot can be obtained.  Repeating the measurements using different mediums ${n}_{i}$, the second plot may be obtained.  And so, $\cfrac{F_o}{{m}_{p}}$ the photon acceleration under the driving force in free space can be approximated.