Polarization: minimum thickness for quater-wave plate

[ProPatto16]

a certain bifringement material has indexes of refraction n₁ and n₂ for the two perpendicular components of linearly polarized light passing through it. the corresponding wavelengths are λ₁=λ₀/n₁ and λ₂=λ₀/n₂, where λ₀ is wavelength in vacuum. If crystal is to function as a quarter-wave plate, the number of wavelengths of each component within a material must differ by 1/4. show that the minimum thickness for a quarter-wave plate is

d=λ₀/[4(n₁-n₂)]

i have no idea. i can see all the numbers are there, but i can't see how to actually "show" it.

thanks

 

[Charles_Chen]

a certain bifringement material has indexes of refraction n₁ and n₂ for the two perpendicular components of linearly polarized light passing through it. the corresponding wavelengths are λ₁=λ₀/n₁ and λ₂=λ₀/n₂, where λ₀ is wavelength in vacuum. If crystal is to function as a quarter-wave plate, the number of wavelengths of each component within a material must differ by 1/4. show that the minimum thickness for a quarter-wave plate is

d=λ₀/[4(n₁-n₂)]

i have no idea. i can see all the numbers are there, but i can't see how to actually "show" it.

thanks

Yes, usually true zero-order wave plate is very thin, <100um depends on wavelength.
The mostly used material is crystal quartz.
What optical wavelength you are using?
Maybe I can help to design, email: charles.chen@photonik.com.sg