The thickness is 155 nm at t1.
The thickness is 77.3 nm at t2.
The inquiry informs us that the laser light's wavelength is λ=510nm
The plastic rod's refractive index is n=1.30
The transparent coating's refractive index is nr=1.65
Minimum reflection would be required for maximal light transmission into the rod, and it is mathematically described as
2t1=510+10⁻⁹/1.65
t1=510+10⁻⁹/1.65*2
t1=155nm
where m is the interference order, which equals 1.
2t2= {m+1/2} λ/nr
The thickness is t replacing values
t1=155 nm
The highest reflection would occur for minimal light penetration through the rod, and this maximum reflection is mathematically described as
2t2= [m+1/2] λ/nr
t2=77.3 nm
The complete question is- Laser light of wavelength 510 nm is traveling in air and shines at normal incidence onto the flat end of a transparent plastic rod that has n = 1.30. The end of the rod has a thin coating of a transparent material that has refractive index 1.65. What is the minimum (nonzero) thickness of the coating (a) for which there is maximum transmission of the light into the rod; (b) for which transmission into the rod is minimized?
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