Young's Two Slit Experiment Question

[Von Neumann]

Question:

I'm sure this is a stupid question, but it has been bothering me lately so I'll ask it anyhow.

In Young's Two Slit experiment the conditions for max and min are

dsin\theta=m\lambda (max)

dsin\theta=(m+\frac{1}{2})\lambda (min)

where m is an integer and d is the separation of the slits and \theta is the angle the lower ray makes with the horizontal.

If the separation d of the slits is much smaller than the distance between the slits and a screen (on which they meet at point), these equations are said to be exact.

However, and this is what confuses me, if parallel light rays are used, the path difference is dsin\theta even if D is not much larger than d. (ie. placing the screen at the focal plane of a converging lens.) If the light rays are parallel, how could they ever focus at a point on the screen? By definition parallel lines never intersect.

I'm obviously misunderstanding something monumental, so I apologize in advance.

 

[Sunil Simha]

This question is not stupid.
You just need to understand that those equations are derived making certain approximations. Check out my attachment.

Firstly, just see the two paths of light. Aren't they almost parallel? Well, not so parallel in my diagram but imagine a real life situation where d is of the order of micrometers and D is measured in meters. Got the picture? That's why people get dsinθ as the path difference. It is just an approximation. They actual rays do meet and are not parallel.

 

[Von Neumann]

The way it was worded by my professor (and his book) conveys the idea as though it is possible for parallel lines to intersect (which really was boggling my mind). I understand. Thanks!