Laser light of wavelength 510 nm is traveling in air andshines at normal incidence onto the flat end of a transparent plasticrod that has n = 1.30. The end of the rod has a thin coating ofa transparent material that has refractive index 1.65. Whatis theminimum (nonzero) thickness of the coating (a) for which thereis maximum transmission of the light into the rod; (b) for whichtransmission into the rod is minimized?

a

The thickness is  

b

 The thickness is  

Explanation:

From the question we are told that

    The wavelength of the laser light is  

    The refractive index of the plastic rod is

    The refractive index of the transparent coating is  

For maximum transmission of light into the rod the reflection would be minimum and this minimum reflection is mathematically represented as

Where m is the order of interference which is equal to 1

           t is the thickness

Substituting values

For minimum transmission of light into the rod the reflection would be maximum and this maximum reflection is mathematically represented as

Where m = 0 this because the transmission of light is minimum

Substituting values