Understanding Double Slit Interference: How Do We Count Fringes?

[lha08]

Homework Statement

When they say the first and third bright fringe, do they mean m=1 and m=0..do we count m=0?
And likewise for when they say first and third dark fringe, is it m=1.5 and m=3.5?
How would we know when to count m=0?
Thanks

Homework Equations

The Attempt at a Solution

 

[Carid]

The central bright fringe is the place when the path length form the two slits is zero.
The dark fringes on each side of this central fringe is where the path lengths differ by half a wavelength.
The bright fringes outside of those is where the path lengths differ by one full wavelength.
And so on...
That's the physics of the thing.
Now what's this character m? Never heard of him.
Suggest you write out some equation where it appears and explain what it stands for.

 

[nlightner]

Great question! When referring to the "first" or "third" bright or dark fringe, they are actually referring to the order of the fringe, not the value of m. The order of the fringe is determined by the number of bright or dark bands present between the central maximum and the desired fringe. So for the first bright fringe, there would be one bright band between the central maximum and the first bright fringe. For the third bright fringe, there would be three bright bands between the central maximum and the third bright fringe.

In terms of counting m, it is typical to start with m=0 at the central maximum and then count outwards from there. So for the first bright fringe, m=1, for the second bright fringe, m=2, and so on. For dark fringes, the counting starts at m=0.5 and goes outwards in increments of 1. So for the first dark fringe, m=0.5, for the second dark fringe, m=1.5, and so on.

It is important to note that the values of m for bright and dark fringes are not always whole numbers. The formula for calculating the position of a bright or dark fringe is given by d*sin(theta) = m*lambda, where d is the slit separation, theta is the angle of diffraction, m is the order of the fringe, and lambda is the wavelength of light. So the value of m can be any real number, not just whole numbers.

I hope this helps clarify the counting of fringes in double slit interference. Let me know if you have any other questions.