The carbonyl C is numbered 1 C because of has higher priority. Thus, you would count going down. The highest numbered Carbon refers to the one with the highest value, as with your example of D-Threose, it is the 3rd Carbon right before the CH2OH. You don't count the CH2OH because it is not chiral. So D refers to dextrarotary meaning right which the OH group IS on the right. And the L-Threose has the OH group on the left, levarotary.
The carbonyl C is numbered 1 C because of has higher priority. Thus, you would count going down. The highest numbered Carbon refers to the one with the highest value, as with your example of D-Threose, it is the 3rd Carbon right before the CH2OH. You don't count the CH2OH because it is not chiral. So D refers to dextrarotary meaning right which the OH group IS on the right. And the L-Threose has the OH group on the left, levarotary.
No! This is an important point you bring up. D and L do not refer to the direction of rotation of plane polarized light. Not capital D and L, anyway, They refer to how the highest numbered chiral center is oriented relative to glyceraldehyde. In glyceraldehyde, D and L were assigned arbitrarily. So it actually does not have anything to do with rotation of plane-polarized light.
One point to mention here is that this is true for the purposes of your response, but you can actually tell that (d)-molecule rotates plane-polarized light to the right. That's because lower-case d means dextrorotatory and is equivalent to (+). This means it rotates light clockwise. However, it's not possible to tell whether a molecule is (+) or (-) just by structure. So if you're ever given (d)-molecule, the passage is telling you that it rotates light clockwise and that this fact was determined by them experimentally.
Okay so here's another question. I understand that levarotary means that the electromagnetic radiation is being turned counterclockwise, but is it being turned counterclockwise from the standpoint of the observer or from the source? If you're standing at the source looking at a light that rotates counterclockwise as it propagates away from you, it will appear to be rotating in the opposite direction when viewed from the detector. Intuition tells me it should be analyzed from the standpoint of the detector, assigning the direction of rotation as the wave propagates toward the detector.
I'm not sure which direction is conventional in practice, but if you think about it closer, it does not matter which way you define as positive or negative as long as everybody follows convention. That is, you could just as easily define positive and negative as being in the opposite directions that they currently are.
@aldol16 So the (-)(+) and the small d and l tell the direction rotation of plane polarized light? And the big D and L just tell how the OH is oriented relative to glyceraldehyde. Is it where I said D meant dextrarotary and L means levarotary that I was incorrect? Because I just meant which way the OH's are facing; did not mean to say the direction, as in the direction of rotation of plane polarized light.
@aldol16 So the (-)(+) and the small d and l tell the direction rotation of plane polarized light? And the big D and L just tell how the OH is oriented relative to glyceraldehyde. Is it where I said D meant dextrarotary and L means levarotary that I was incorrect? Because I just meant which way the OH's are facing; did not mean to say the direction, as in the direction of rotation of plane polarized light.
Yes, exactly. Little d and l refer to dextro- or levo-rotatory and these inherently give you the direction of rotation of plane-polarized light. Big D and L are not related to dextro- or levo-rotation at all and instead refer to relative orientation compared to glyceraldehyde. So you should just use big D and L and don't worry about little d and l in this case because you don't know which direction the enantiomers rotate light.
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