Three bright fringes

1. The problem statement, all variables and given/known data
One glass plate sits flat and another is above it inclined on an angle(shown on diagram provided). monochromatic λ light shines on it. The fringes are spaced p apart, and the bottom plate is length d.
Between t1 and t2 there are three bright fringes apart.

What is (t1-t2) ?

2. Relevant equations

[tex] m\lambda_o=2n_f t\cos\theta_t+\frac{\lambda_o}{2}[/tex]

3. The attempt at a solution
I’m not sure if what I did is valid because when I modeled it I did not take into account the glass plate on the bottom moving up to where I modeled it. Also this does not take into account the given distance between the fringes, p, explicitly which is another reason to why I think my solution may be incorrect.

[tex] m\lambda_o=2n_f t\cos\theta_t+\frac{\lambda_o}{2}[/tex]
plug in 3 for the m fringes, also use t=t1-t2 for the heights of the plates. approximate theta as 0

[tex]3\lambda_o=2n_f (t_1-t_2)+\frac{\lambda_o}{2}\\

\frac{1}{2n_f}[3\lambda_o-\frac{\lambda_o}{2}]= (t_1-t_2) [/tex]

I’m pretty sure this is incorrect but do not know how else to attack the problem.

Any help would be much appreciated.

Attached Images
File Type: png two glass plates.png (2.8 KB)

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