# Why in professional spectroscopes diffraction gratings are used instead of prisms?

Why in professional spectroscopes diffraction gratings are used instead of prisms?

I guess transparency is not an issue, as we need optics anyway.

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Just compare the resolution of the two:

• Prism depending on n, there is no good material n>1.7 (besides diamond)
• depending on base length if you use a equilateral triangle
• have to use more than one to overcome this
• prism absorb light, you have got scattering (stray light) too

Now a grating:

• optimize it for your wavelength
• choose lines per milimeter
• resolution depending on the number of lines that are illuminated
• compact device
• just transmission gratings have got absorption, you can do your measurement in reflection with a blazed grating
• design your blazed grating to get the most light in e.g. 2nd order

Quantitatively

Prism: $\frac{\lambda}{\Delta \lambda} = t \frac{dn}{d\lambda}$

Grating: $\frac{\lambda}{\Delta \lambda} = \frac{zD}{g}=zN$

where t is your base length, z... order of spectrum, g...grating constant, D...entrance beam diameter, N...number of illuminated lines

So just use a grating, nowadays they can be fabricated in excellent quality. On my university learning the pros of a diffraction grating is part of the 1st year laboratory exercises.

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As I can't comment on the answer of @anna v The link to the prism manufacturer is bogus. They claim that prism are better because gratings have got multiple spectrums. This is not true! You do also have got multiple spectrums on a prism, because there are a lot of internal reflections. You must be really carefull do not use a false spectrum by following the rotation against or in direction of the rotation of the prism. Most of the light is always in 1st order. Transmission gratings have got a final number of orders because diffraction above 90° is not possible. - part 1 - –  Alex1167623 Feb 8 '12 at 20:08
- part 2 - However you can design a blazed grating to get the most intensity in 2nd order and nothing is lost in 0th order. –  Alex1167623 Feb 8 '12 at 20:12
A quibble. There are plenty of good optical glasses above $n=1.7$. However, in general the higher in index you go, the more dispersive they get. One of my favourite glasses to design with is Schott N-LASF31A: it has a refractive index of about 1.9 and an Abbe number of 41 - most glasses of this index are much more dispersive than this. Great answer, though, +1 –  WetSavannaAnimal aka Rod Vance Apr 22 at 11:39

I found a comparison of the two possibilities and it seems that prisms are better.

This manual for a spectroscope used for jewelry stones, gives higher marks to the diffraction grating towards the red part of the spectrum, where the crystal gets lower efficiency. It seems the efficiency for the grating is uniform for the whole spectrum. It is also possible that economically it might be cheaper to use a grating than three crystals, as this particular brand proposes to solve the efficiency for crystals.

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One reason prisms are not preferred is that their quality is directly proportional to their size; if you want to make a decent spectroscope using a prism, you may not be able to carry it.

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