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Old Dec 2nd 2013, 09:10 PM   #1
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Diffraction Grating

Does anyone know the explanation of this question?
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Old Dec 3rd 2013, 06:44 AM   #2
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Originally Posted by engchunh View Post
Does anyone know the explanation of this question?
Typically when something is supposed to be symmetric and isn't then there's something wrong with the equipment...

-Dan
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Old Dec 3rd 2013, 09:33 AM   #3
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A famous Sherlock Holmes quote is:
"when you have eliminated everything that is impossible, whatever is left (no matter how improbable) must be the truth.

I often find this is also the key to solving multiple choice problems.

It is so long since I did diffraction gratings at school that im not entirely sure of the answer myself, however:
There is one choice that (in my opinion) requires almost zero thought to discard,
There is another that I am happy to discard after just a little consideration,
Taking the remaining two, one seems much more likely to be the source of experimental error than the other.
Finally applying my hazy recollections to these 2 remaining choices,
I am fairly sure that the one that I have marked as unlikely to be a source of experimental error would not produce the observed effect anyway.

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Old Dec 3rd 2013, 07:07 PM   #4
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So would the answer be D, something wrong with the equipment (slits?)
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Old Dec 4th 2013, 09:16 AM   #5
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I'm actually not entirely sure...

My first discard was C,
just by looking atthe supplied drawing (with no knowledge of physics required) it can be seen that moving the screen back and forth will make no difference to the 2 angles.

My second discard was A,
If wavelength 1 produces a symmetrical pattern, and wavelength 2 also produces a symmetrical pattern, then whatever the 2 patterns look like when superimposed, it will also be symetrical, so the two angles will be the same.

This leaves B and D.

I personally favour B...
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Old Dec 4th 2013, 09:55 AM   #6
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Good analysis, MBW. I'm leaning toward D though. Think of it this way...you can't get the diffraction grating and laser beam exactly perpendicular and you will still see the correct symmetry. That doesn't mean that the symmetry won't break down if you take "extreme" angles between the grating and laser beam, but I wouldn't regard the angle as a potential problem.

Also check here for the non-perpendicular case.

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Old Dec 4th 2013, 10:55 AM   #7
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Quoting from your wikipedia link:

when light is normally incident on the grating, the diffracted light will have maxima at angles θm given by:
d sin(θm) = mλ
It is straightforward to show that if a plane wave is incident at any arbitrary angle θi, the grating equation becomes:
d sin(θm + θi) = mλ
When solved for the diffracted angle maxima, the equation is:
θm=arcsin[mλ/d +sin(θi)]

If m=1 this gives:
θ1=arcsin[λ/d +sin(θi)]
If m=-1 this gives:
θ-1=arcsin[-λ/d +sin(θi)]

Surely arcsin[λ/d +sin(θi)] ≠ -arcsin[-λ/d +sin(θi)]
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Old Dec 4th 2013, 10:57 AM   #8
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Red face oops

Just noticed my mistake:
θ0=arcsin[sin(θi)]

thus the angle ether side of the zero point remains the same.
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Old Jan 1st 2014, 10:39 PM   #9
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I have read this.......its amazing and i am really impressed.Thanks for sharing this nice info.
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Old Sep 23rd 2014, 04:03 AM   #10
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Originally Posted by engchunh View Post
Does anyone know the explanation of this question?
The diffraction formula is

d (sin α + sin θ) = m λ

d: Groove spacing

α: Angle between the incoming light and the normal of the grating

θ: Angle between the difracted light and the normal of the grating

m: Order

λ: Wavelength

If the angle of incidence is perpendicular to the grating, the |θ| must be the same for m=-1 and m=+1.

If θ differs for these two orders (i.e. m=-1 and m=+1), which is the case here, that means the angle of incidence is not perpendicular to the grating.

So the answer is B.
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