PX154 - I6 - transmission and reflection coefficients for light

only normal incidence will be considered (ie: $θ_{i} = 0 °$ ), and polarization neglected
for waves on joined strings , the amplitudes: if $μ_{1} < μ_{2}$ , the reflected wave was inverted
here, intensities will be considered: [YF eqn 32.4]

I = \frac{1}{2} ϵ_{0} c E^{2}

where, $E =$ E-filed amplitude

T = \frac{4 n_{i} n_{t}}{(n_{i} + n_{t})^{2}} a n d R = \frac{(n_{i} - n_{t})^{2}}{(n_{i} + n_{t})^{2}}

eg: for $a i r \to g l a s s : T = 0.96, R = 0.04$
- when light leaves the glass, the same result is obtained
- for a sheet of glass with two surfaces: $T = 0.92$
eg: diamond:
- air $: n = 1$ , diamond $: n = 2.4 ⟹ T = 0.83$
eg: $a i r (n = 1) \to g l a s s (n = 1.5) \to d i a m o n d (n = 2.4)$
- $T_{a i r \to g l a s s} = 0.96$ , $T_{g l a s s \to d i a m o n d} = 0.95$
- total transmission, $T = 0.96 \times 0.95 = 0.91$
  - transmission is increased by using a material of intermediate refractive index (eg: $n_{i} = n_{t} ⟹ T = 1$ )
    - vital in optics
    - concept of "impedance matching"