Supporting Information
We can solve for the average refractive index of the polystyrene particle film layer using
the Maxwell-Garnett Effective Medium Approximation:
 eff   m

2(1   i ) m  (1 2 i ) i
(2   i ) m  (1   i ) i
(Equation 1)
where e m and e i are the dielectric constants for polystyrene and air respectively and
f i represents the filling fraction of the air. By using the square of the refractive index as
the dielectric constant, we have e m = 2.56, e i = 1, f i = 0.3, we find  eff = 2.01. Taking
the square root, we find neff = 1.42

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For normal incidence, the Fresnel reflection between two interfaces is given by the
following formula:
n1  n 2 2
R  

n1  n 2 
(Equation 2)
We solve for R in order to obtain a value for the reflected intensity between air and a

layer of polystyrene particles. Using n1 = 1.42 (polystyrene with air inclusions) and n2 =
1 (air), R = 0.03 corresponding to 3% reflectance. This corresponds to specular
reflection. The error in the measurement from the spectrophotometer can be attributed to
background diffuse reflection.