# Maxima in a diffraction grating

• L_landau
In summary, a diffraction grating with 300 nm slit width and 900 nm separation is illuminated by 600 nm monochromatic waves. To find the number of maxima in the diffraction pattern, the equation mλ = dsinθ can be used. However, to properly account for the spacing between slits, the equation (a+b)sinθ = mλ is used, where a and b are the slit width and separation, respectively.
L_landau

## Homework Statement

A diffraction grating is made up of slits of width 300 nm with separation 900 nm. The grating is illuminated by monochromatic plane waves of wavelength l 600 nm at normal incidence. How many maxima are there in the full diffraction pattern?

mλ = dsinθ

## The Attempt at a Solution

I thought that I could just use the above equation and doing so I get m = 1.5. However, the solution uses
(a+b)sinθ = mλ . Can I really just add the slit width and the separation width like that?

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You need the distance between the centers of adjacent slits, if 900 nm is the space between their edges you have to add the slit width.

Oh that makes sense! Thank you!

## 1. What is a diffraction grating?

A diffraction grating is an optical component that contains a large number of parallel, equally spaced grooves or slits. It is used to separate light into its component wavelengths, creating a spectrum.

## 2. How do maxima occur in a diffraction grating?

Maxima occur in a diffraction grating when the light passing through the grating is diffracted at specific angles, producing bright spots. These angles are determined by the spacing of the grating and the wavelength of the incident light.

## 3. What is the significance of maxima in a diffraction grating?

The maxima in a diffraction grating are important because they allow for the precise measurement of wavelengths of light. By observing the angles at which the maxima occur, the wavelength of the incident light can be determined.

## 4. Can the number of maxima be controlled in a diffraction grating?

Yes, the number of maxima in a diffraction grating can be controlled by adjusting the spacing of the grooves or slits. A grating with a higher number of slits will produce more maxima, while a grating with fewer slits will produce fewer maxima.

## 5. How is the intensity of the maxima in a diffraction grating affected?

The intensity of the maxima in a diffraction grating is affected by several factors, including the angle of incidence, the spacing of the grating, and the wavelength of the incident light. Generally, the intensity of the maxima increases as the angle of incidence and the number of slits increase, and decreases as the wavelength of the incident light increases.

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