ANSWER
[tex]500\text{ nm}[/tex]EXPLANATION
To find the second longest wavelength that reflects brightly from the film, apply the expression for constructive interference:
[tex]2nt+\frac{\lambda}{2}=m\lambda[/tex]where m = 2
n = refractive index
λ = wavelength
Make λ the subject of the formula:
[tex]\begin{gathered} 2nt=mλ-\frac{λ}{2} \\ \\ 2nt=(2m-1)\frac{λ}{2} \\ \\ \frac{λ}{2}=\frac{2nt}{2m-1} \\ \\ λ=\frac{4nt}{2m-1} \end{gathered}[/tex]Now, calculate the wavelength by substituting the given values into the equation:
[tex]\begin{gathered} λ=\frac{4*1.42*264}{2(2)-1} \\ \\ λ=\frac{1499.52}{4-1}=\frac{1499.52}{3} \\ \\ λ=499.84\text{ nm}\approx500\text{ nm} \end{gathered}[/tex]That is the answer.
