A problem involving thin film interference

[lorenz0]

Homework Statement

A blue ($\lambda=450nm$) beam of light hits a glass plate with $n_g=1.5$. Calculate the minimum thickness that a plate with refractive index $n_F=1.33$, that must be placed between the air and the glass to produce the maximum intensity reflected in the blue, should have. How much would this thickness have to be if the light was coming from the glass towards the air?

Relevant Equations

$\lambda_{medium}=\frac{\lambda}{n_{medium}}$

I know that every time that light goes from traveling through a medium with lower refractive index to one with a higher refractive index the reflected light undergoes a $\frac{\lambda}{2}$ phase change. Since this happens both at the air-plate and plate-glass interfaces we have that the phase changes cancel each other out and the condition for constructive interference is (where $t$ denotes the thickness of the plate): $2t=m \lambda_{plate}\Leftrightarrow 2t=m\frac{\lambda}{n_F}\Leftrightarrow t=\frac{m\lambda}{2n_F}$ so the minimum (non-zero) thickness is $t=\frac{\lambda}{2n_F}.$

In the second scenario the situation is reversed and there is no $\frac{\lambda}{2}$ phase change for both the glass-plate interface and the plate-air interface and so the condition for constructive interference again reads $2t=m \lambda_{plate}$ and we get the same result as before.

Is this correct? I still have to fully grasp this phenomenon and I would like to have feedback on the way I have reasoned about this problem, thanks.

 

[kuruman]

Your reasoning is correct.

 

[lorenz0]

Your reasoning is correct.

Thanks!