Problem 12.2 Light of wavelength A in a medium of refractive index n₁, is normally incident on a thin film of refractive index n2 and optical thickness X/4 which coats a plane substrate of refractive index n3. Show that the film is a perfect anti-reflector (r = 0) if n² = n₁n3.
Problem 12.2 Light of wavelength A in a medium of refractive index n₁, is normally incident on a thin film of refractive index n2 and optical thickness X/4 which coats a plane substrate of refractive index n3. Show that the film is a perfect anti-reflector (r = 0) if n² = n₁n3.
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Please elaborate solution of 12.2
Transcribed Image Text:12.2
The matrix relating reflection coefficient and transmission coefficient t for the
2/4 film is given by:
cos
isin 8/m₂
0i/n₂
in, sin d
cos 8
in₂ 0
where the phase change
= 7/2 for the 2/4 film.
Following the analysis in text page 352, we can find the coefficient A and B are
given by:
A= n₁(M₁₁ + M₁n₂) = in.nz/n₂
Ⓒ2008 John Wiley & Sons, Ltd
B = (M₂1+M₂23) = in₂
A perfect anti-reflector requires:
A-B_inn/n₂- in₂
R=
=
A+B inn/n₂ + in₂
which gives:
n = nin
M =
Transcribed Image Text:Problem 12.2
Light of wavelength A in a medium of refractive index n₁ is normally incident on a thin film of
refractive index n₂ and optical thickness X/4 which coats a plane substrate of refractive index n3.
Show that the film is a perfect anti-reflector (r = 0) if n2 = n₁nz.
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