# Diffraction with a large array of slits

• Flucky
In summary, the conversation discusses a question about the diffraction of light through a screen with slits of equal width and periodic displacement. The question asks for the maximum diffraction order that can be observed and the minimum period for which diffraction can be observed for a specific wavelength of light. The relevant equation is asinθ = mλ, and there is also a mention of sinθ\pm1 = \pm\frac{λ}{b} without explanation. The discussion mentions looking at articles and applets, but the question still remains unanswered with three unknown variables.
Flucky
Hi all, exams soon and I'm stressing out over this small question. If anyone could guide me through, explaining why you're doing what you're doing that'd be beyond great.

## Homework Statement

Light of wavelength λ is incident normally on a screen with a large array of slits having
equal widths b, and periodically displaced by a distance a.

(i) Find the maximum diﬀraction order which can be observed using this system of slits.

(ii) Find the minimum period a for which diﬀraction can be observed for light with
wavelength λ = 10µm.

## Homework Equations

AFAIK the only equation relevant is asinθ = mλ

One that has cropped up is sinθ$\pm1$ = $\pm\frac{λ}{b}$ , although there is no explanation next to this one so I'm not sure what it means.

## The Attempt at a Solution

Initial thoughts are to set θ = 90° as it's asking for a maximum. Past this I don't know where to go

It's not hard to find articles on the subject on the net. Did you try to follow any of those?

I've had a look all round but can't seem to find anything that helps, unless I'm missing something obvious. I've played around with a few applets as well. The things I found focused on the first equation, and the questions would often be "find the #th maxima" with slit width etc given.

The 90 degrees being a maximum I understand and max diffraction occurs when the slit width equals the wavelength, but for the first part of the question that still leaves me with 3 unknown variables.

Also I created another thread over in the other HW section (https://www.physicsforums.com/showthread.php?p=4758792) thinking I could delete this one. Don't know if the mods would like to merge/delete one.

## What is diffraction?

Diffraction is the bending or spreading of waves as they pass through an opening or around an obstacle. It is a characteristic behavior of all types of waves, including light, sound, and water waves.

## What is a large array of slits?

A large array of slits refers to a structure with multiple parallel slits or openings that are very close together. This setup is commonly used in experiments to study diffraction patterns.

## How does diffraction occur with a large array of slits?

When a wave, such as light, passes through a large array of slits, it diffracts or spreads out in different directions. This is due to the interference of the waves passing through the slits, creating a pattern of bright and dark spots known as a diffraction pattern.

## What factors affect the diffraction pattern of a large array of slits?

The diffraction pattern of a large array of slits is affected by several factors, including the spacing between the slits, the wavelength of the incident wave, and the size of the slits. Changing these parameters can alter the shape and intensity of the diffraction pattern.

## How is diffraction with a large array of slits used in science and technology?

Diffraction with a large array of slits is used in many fields, including optics, acoustics, and radio waves. It is an essential tool for studying the characteristics of waves and can be applied in various technologies, such as diffraction gratings in spectrometers and antennas for wireless communication.

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