Answer:
a
The thickness is [tex]t_1 = 155nm[/tex]
b
The thickness is [tex]t_2 =77.3 nm[/tex]
Explanation:
From the question we are told that
The wavelength of the laser light is [tex]\lambda = 510 nm = 510*10^{-9} m[/tex]
The refractive index of the plastic rod is [tex]n = 1.30[/tex]
The refractive index of the transparent coating is [tex]n__{T}} = 1.65[/tex]
For maximum transmission of light into the rod the reflection would be minimum and this minimum reflection is mathematically represented as
[tex]2 t_1 = m \frac{\lambda }{n___{T}}}[/tex]
Where m is the order of interference which is equal to 1
t is the thickness
Substituting values
[tex]2 t_1 = \frac{510*10^{-9}}{1.65}[/tex]
[tex]t_1 = \frac{510*10^{-9}}{ 2 * 1.65}[/tex]
[tex]t_1 = 155nm[/tex]
For minimum transmission of light into the rod the reflection would be maximum and this maximum reflection is mathematically represented as
[tex]2t_2 = [ m + \frac{1}{2} ] \frac{\lambda }{n__{T}}}[/tex]
Where m = 0 this because the transmission of light is minimum
Substituting values
[tex]2t_2 = [ 0 + \frac{1}{2} ] \frac{510 *10^{-9} }{1.65}[/tex]
[tex]t_2 = [ 0 + \frac{1}{2} ] \frac{510 *10^{-9} }{ 2 * 1.65}[/tex]
[tex]t_2 =77.3 nm[/tex]
