Topics: Purdue ME 606: Reflection from Surfaces

Purdue ME 606: Reflection from Surfaces

Specular reflection from ideal surfaces

$θ i = θ r$

$d ω i = d ω r$

Occurs for flat clean surfaces

$σ$ = Standard deviation of surface height

For a surface to be smooth

$\frac{\sigma }{\lambda } \ll 1$

Diffuse Reflection

$I r$ =constant

$\frac{\sigma }{\lambda } \gg 1$

Real surface Reflection

Near-normal incident angles

-Approach above limits

-Superposition is possible

Large incident angles

-Diffuses approximately breaks down

-Forward scattering observed

Reflectance

Specular reflectance

$θ i = θ r$

$\rho _s(\theta _i )=\frac{{I_r (\theta _r =\theta _i )}}{{I_i (\theta _i )}}$

Reflection from non-metals

$\rho _{s \bot }=\frac{{\tan ^2 (\theta _1 - \theta _2 )}}{{\tan ^2 (\theta _1 + \theta _2 )}}$

$\rho _{s\parallel }=\frac{{\sin ^2 (\theta _1 - \theta _2 )}}{{\sin ^2 (\theta _1 + \theta _2 )}}$

Relate with Snell’s Law

$sin(θ 1) = n 21 sin(θ 2)$

$n_{21}=\frac{{n_2 }}{{n_1 }}$

= Index of refraction

$\rho _s = \frac{1}{2}(\rho _{s \bot } + \rho _{s\parallel } )$

For metals

Considering waves from vacuum (n=1)

$n_{21}=\frac{{n_2 }}{{n_1 }}$

$n 2 = n$

For normal incidence

$\rho _\parallel = \rho _ \bot = \frac{{(n - 1)^2 + \kappa^2 }}{{(n - 1)^2 + \kappa^2 }}$

- check this equation

for $θ i = 0$

$κ$ =Absorption coefficient

More algebraic complication for non-normal angles of incidence

Last modified on 14 Dec, 2008

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