How to prove the two angles are equal?

Question

It is from Young Double slit experiment. But How to prove the the two $\theta$ are equal, I meant, how $\angle EAD= \angle PEC$? I see from the both triagle have $90^0$ but what about others.

If we think θ→0 we get valid results. we can see the image from any article whoch is YOUNG's double slit experiment. citycollegiate.com/interference2.htm

Answer 1

I believe both the angles can be equal only when L is infinity. Here is why---

If ∠PEC = θ then ∠AEP = 90 - θ

So in small triangle AEO where O is the point of intersection of EP and AD :--

∠AOE = 180 - (θ + 90 - θ) = 90

Now because ∠AOE = ∠ADB = 90 so it follows that EP and BP are parallel. It is only possible when L is infinity.

Does the answer make sense to you...??

Answer 2

The fact that the angles are 'equal' is based on the assumption given in the original post.

It says "Since the value of 'd' is very very small as compared to L, therefore, θ will also be very small. In this condition we can assume that : sin θ = tan θ".