ANSWER
[tex]\begin{equation*} 333\text{ }nm \end{equation*}[/tex]EXPLANATION
Parameters given:
Wavelength of the light, λ = 666 nm = 666 * 10^(-9) m
θ = 90°
n = 1
To find the minimum distance such that the light transmitted through the right is a maximum, we apply the formula:
[tex]\sin\theta=\frac{n\lambda}{2d}[/tex]where d = minimum distance.
Therefore, solving for d, we have that the minimum distance is:
[tex]\begin{gathered} \sin90=\frac{1*666*10^{-9}}{2*d} \\ \\ 1=\frac{666*10^{-9}}{2*d} \\ \\ d=\frac{666*10^{-9}}{2} \\ \\ d=333*10^{-9}\text{ }m=333\text{ }nm \end{gathered}[/tex]That is the answer.
