PX154 - I5 - snell's law

snell's law:

n_{1} \sin θ_{i} = n_{2} \sin θ_{t}

for the reflected ray,

θ_{i} = θ_{r}

if $n_{i} < n_{t}$ , then $θ_{i} > θ_{t}$
if $n_{i} > n_{t}$ , then $θ_{i} < θ_{2}$ (eg: a light ray in water hitting its surface)
- a total internal reflection can be obtained

total internal reflection

from $n_{i} \sin θ_{i} = n_{t} \sin θ_{t}$ ,

\sin θ_{t} = \frac{n_{i}}{n_{t}} \sin θ_{i}

if $θ_{t} = 90 ° : \sin θ_{t} = 1$
- $\sin θ_{i} = \frac{n_{t}}{n_{i}} = \sin θ_{c}$ , where $θ_{c} =$ critical angle
- if $\sin θ_{i} > \frac{n_{t}}{n_{i}} :$ no transmission

brewster's law

polarization by reflection: if the angle between $r_{t}$ and $r_{r}$ is $90 °$
from snell's law:

\tan θ_{i} = \frac{n_{t}}{n_{i}}

- this is brewster's law
- for polarization, this is known as the "polarization angle", $θ_{p}$
- for $a i r \to g l a s s : θ_{p} = 56.3 °$
- frenel equations will be needed to study this in more detail

dispersion

refractive index can depend on the wavelength/frequency
snell's law conveys that light of different wavelengths will have different transmission angles (eg: rainbows, prism)