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Diffraction Gratings

A grating spectrometer is used at normal incidence to observe the light from a sodium flame. A strong yellow line is seen in the first order when the telescope axis is at an angle of 16.43 to the normal to the grating.
What is the highest order in which the line can be seen?

=/ This seems like a wierd question. It gives a value for the line spacing later on in the question, but it seems that we're not supposed to use it for this part. Please help!

Reply 1

steelmole

highest order? what's that fancy speak for?

Reply 2

TheRandomer

Worked it out now, question was just stupidly put together. haha.

Reply 3

TheRandomer

steelmole

highest order? what's that fancy speak for?

The big maxima bits on the diffraction pattern.. when they get so thin they're just lines they're called orders. I think... :smile:

Reply 4

steelmole

Can you just tell me your answer so I can understand it a bit better?

Reply 5

TheRandomer

steelmole

Can you just tell me your answer so I can understand it a bit better?

Sure :]

Okay so the formula for the diffraction grating is:
dsin(x)=n(wavelength)
[d is the spacing of lines in the grating, x is the angle from the horizontal, n is the 'order' and wavelength is.. yeah.. :p:

)

It says the grating has 4800 lines per cm, so since d=1/(# of lines per m)
d=1/480000
= 2.083 x 10^-6 m

rearrange and you get:
wavelength= [dsin(x)]/n
= 2.083x10^-6 x sin16.43
= 5.89 x 10^-7 m

the maximum angle you can have from the horizontal when you diffract something is 90 degrees [obv it can't come back at you!] so when x=90 we get:
n=d/wavelength = 3.54

you'll have orders on either side of the centre, so basically you can have x degrees 'up' from the normal, or x degrees 'down', and there's also the one in the middle, produced when light goes straight through. So the maximum number of orders = 3x2 + 1
= 7

[when i say horizontal etc. i mean relative to my diagram.. not sure how a real spectrometer is]

Reply 6

steelmole