A certain birefringent material has indexes of refraction n1, and n2 for the two perpendicular components of linearly polarized light passing through it. The corresponding wavelengths are ?, = ?0/n1, and ?0/n2, where Ao is the wavelength in vacuum.(a) If the crystal is to function as a quarter-wave plate, the number of wavelengths of each component within the material must differ by ?. Show that the minimum thickness for a quarter-wave plate is(b) Find the minimum thickness of a quarter-wave plate made of siderite (Fe O ?? CO2) if the indexes of refraction are n1 = 1.875 and n2 = 1.635 and the wavelength in vacuum is Ao = 589nm.

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d= λο 4(n = m2)