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**1. Homework Statement**

I need help on figuring out part C which is determining the ratio between ##t_1## and ##t_2## in order to get constructive interference. I'm given the index of refractions ##n_1=1.5## and ##n_2=2## and that I know that wave 1 and 2 have half cycle shift and wave 3 does not.

I only really need help with part c since I figured out the rest.

**2. Homework Equations**

1. ##2t=(m+.5)λ##

2. ##2t=(m)λ##

**3. The Attempt at a Solution**

I basically did the same thing for how I did part b. Since both ray 1 and 2 have shifts, I used the 2nd equation. And for ray 2 and 3, I used the 1st equation since there is a pi difference.

$$2t_1=(m+.5)(\lambda/n_1)$$ and set m =0 since we want minimum t thickness.

$$2t_2=m(\lambda/n_2)$$ and set m =1 since we want minimum thickness also.

so

$$2t_1=\lambda/(2(n_1))$$

$$2t_2=\lambda/n_2$$

then I divide both ##2t_1## and ##2t_2## so I have this:

##t_1/t_2=n_2/2n_1## since the 2s and ##\lambda## cancel out.

Since ##n_1=1.5## and ##n_2=2##,

$$t_1/t_2=2/2(1.5)$$ therefore ##t_1/t_2=2/3##

However, the solutions say it is ##t_1/t_2=2n_2/5n_1=2*2/5*1.5=0.5333##

I don't get how I did the same method for constructive yet can't use it for destructive.