Quick help with math in thin film problem

[Anuj68]

Homework Statement

(1 / 2) (λ1 /nfilm) (m1) = (1 /4) (λ2 / nfilm) (2m2 +1)

(2*m2 + 1) / (2*m1) =λ1 / λ2 = 640 nm / 512 nm = 1.25

We want to solve for m1 and m2.
I have realized that using m1=m2=2 works but I can't figure out how to reach this conclusion mathematically.

Please, any help will be greatly appreciated.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi Anuj68! Welcome to PF!

(try using the X₂ icon just above the Reply box )

(2*m2 + 1) / (2*m1) =λ1 / λ2 = 640 nm / 512 nm = 1.25

We want to solve for m1 and m2.
I have realized that using m1=m2=2 works but I can't figure out how to reach this conclusion mathematically.

(2m₂ + 1)/(2m₁) = 1.25

ie (m₂ + 0.5)/(m₁) = 1.25.

so m₂ = 1.25m₁ - 0.5