Circular Aperture Fresnel Diffraction

[tms1991]

Homework Statement

A circular aperture, with diameter 3.1 mm, is illuminated by a monochromatic plain wave. On the screen, which lays 1m ahead, we observe that the center of the diffraction pattern is dark. When we start to move the screen gradually backwards, the center becomes bright, then dark again and then bright from now on, even if we continue moving the screen. Which is te wavelength of the light we are using in this experiment?

Homework Equations

I would say:

The Rayleigh criterion: sen$$\theta$$ = 1,22 $$\lambda$$/a

The radius of Fresnel`s zone plates: r = [lambda. n. D]^[1/2]

The Attempt at a Solution

My attempt was to make the radius of the third fresnel zone equal to the second minimum of the diffraction pattern. But then I realized it wasn`t as simple as i thought, as the formula of the minima for a circular diffraction pattern is not so simple.
I have no clue now, though I know the answer must be 600.6 nm, I can`t get there. If anyone could help me, I would aprecciate it very much.

PS: sorry for the English...

 

[anathema]

Thank you for your question. Based on the given information, we can use the Rayleigh criterion to determine the wavelength of the light being used in this experiment. The Rayleigh criterion states that the first minimum of the diffraction pattern occurs when the angle between the center of the aperture and the first minimum is equal to 1.22 times the wavelength divided by the diameter of the aperture. In this case, the diameter of the aperture is 3.1 mm, or 0.0031 m. We can rearrange the equation to solve for the wavelength:

wavelength = (1.22 * diameter) / angle

Since the first minimum occurs at an angle of 0.0 degrees (directly ahead of the aperture), we can plug in the values to get:

wavelength = (1.22 * 0.0031 m) / 0.0 degrees

This gives us a wavelength of 600.6 nm, which is the same as the answer you were given. Therefore, the light being used in this experiment has a wavelength of 600.6 nm. I hope this helps! Let me know if you have any further questions.