Respuesta :
Answer:
The thickness of the film, t = 470.59 nm
Explanation:
[tex]\lambda_{film} = \frac{\lambda}{n_{film} }[/tex]
For constructive interference, the net phase change, [tex]\phi = \phi_{2} - \phi_{1} = 2\pi m_{1}[/tex]
Then the thickness, [tex]t = 0.5 \lambda_{film} m_{1}[/tex]
m₁ = 1,2,3........
[tex]t = 0.5\frac{\lambda_{1} }{n_{film} } m_{1}[/tex]..............(i)
For destructive interference, the net phase change is [tex]\phi = \phi_{2} - \phi_{1} = 2(m_{2} + 1)\pi[/tex]
m₂ = 1,2,3........
thickness, [tex]t = 0.5\frac{\lambda_{1} }{n_{film} }(2 m_{2}+1)[/tex]..............(ii)
Equating (i) and (ii)
[tex]0.5\frac{\lambda_{1} }{n_{film} } m_{1} = 0.5\frac{\lambda_{1} }{n_{film} }(2 m_{2}+1)[/tex]
[tex]\frac{2m_{2} + 1}{2m_{1} } = \frac{\lambda_{1} }{\lambda_{2}} = \frac{640}{512}[/tex]
[tex]\frac{2m_{2} + 1}{2m_{1} } = 1.25[/tex].............(iii)
From (iii), When m₁ =2, m₂ = 2
The thickness , [tex]t = 0.5\frac{\lambda_{1} }{n_{film} } m_{1}[/tex] then becomes
[tex]t = 0.5\frac{640}{1.36} *2[/tex]
t = 470.59 nm
