# Unit 2 Section 3 Diffraction Gratings

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## Diffraction Grating

Diffraction Grating: A slide or other thin object that contains lots of equally spaced slits very close together, used to show diffraction patterns of waves.

• When monochromatic light is passed through a diffraction grating with hundreds of slits per milimeter at right angles to the grating, the interference pattern is really sharp because there are so many beams reinforcing the pattern.
• Sharper fringes make for more accurate measurements.

• There is a fringe/line of maximum brightness at the centre called the zero order line - which is in the same direction as the incident on the grating.
• The lines just either side of the central one are called first order lines. The next pair are called the second order and so on.
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## Derivation of the Diffraction Grating Equation - p

Calculate the wavelength of light used in diffraction using:

• d x sin(theta) = n x landa
• d = distance between slits in m
• theta = angle to the normal made by the maximum in degrees or radians
• n = order of maximum
• landa = wavelength of light source in m
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## Derivation of the Diffraction Grating Equation - p

Consider the first order maximum. This happens at the angle where the waves from one slit line up with waves from the next slit that are exactly one wavelength behind.

Call the angle between the first order maximum and the incoming light, theta. The angle between d and the incident of light is the same theta but of an imaginary triangle, d is the slit spacing (hypoteneuse), and the path difference is landa (opposite).

So for the first maximum, sin(theta) = opposite / hypoteneuse = landa / d, so d x sin(theta) = landa

So the other maxima occur when the path difference is 2landa, 3landa, 4landa, etc. So the nth order maximum occurs when the path difference is n x landa.

So to make the equation general, just replace landa with n x landa, where n is an integer - the order of the maximum (the order number): d x sin(theta) = n x landa

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## Derivation of the Diffraction Grating Equation - p

From this equation you can draw a few conclusions:

• If landa Is bigger, sin(theta)is bigger, and so theta is bigger. This means that the larger the wavelength, the more the pattern will spread out.
• If d is bigger, sin(theta) is smaller. This means that the coarser the grating, the less pattern will spread out.
• Values of sin(theta) greater than 1 are impossible. So if for a certain n you get a result of more than 1 for sin(theta) you know that that order doesn't exist.
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## White Light Spectra

If you diffract white light through a diffraction grating then the patterns due to different wavelengths within the white light are spread out by different amounts.

Each order in the pattern becomes a spectrum, with red on the outside and violet on the inside. The zero order maximum stays white because all the wavelengths just pass straight through.

When you split up light from a star using a diffraction grating, you can see line absorption spectra - spectra with dark lines corresponding to different wavelengths of light that have been absorbed.

Each element in a star's atmosphere absorbs light of a different wavelength. So you can compare an absorption line spectrum from an object with spectra from different elements, or different objects made up of known elements, to see what elements that object contains.

Astronomers analyse the spectra of stars and chemists analyse the spectra of certain materials to see what elements are present.

They use diffraction gratings rather than prisms because they're more accurate.

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