[chanelo]

So I'm trying to find d, the space between grooves of a diffraction grating, but I don't know how to isolate it! For this equation:
wavelength = d (a / a² + l²)
I've found a, l, and wavelength. I tried switching wavelength with d by adding a negative in front of
wavelength:
d = -wavelength (a / a² + l²)
but I'm not sure if this is right or not?

[Jorriss]

So... I may not understand what you want.

wavelength = d (a / a2 + l2) seems to imply d = wavelength / (a / a2 + l2).

You just divide by (a / a2 + l2). Am I misunderstanding?

[chanelo]

Ok so for:
589.33 = d (244,000,000 / 244,000,000² + 400,000,000²),
I needed to isolate d so I rearranged the equation to:
d = 589.33 (244,000,000² + 400,000,000² / 244,000,000)
and got 530,242,421,639. Can someone tell me if I rearranged the equation properly and if I have, check my answer? Thanks!

[Borek]

First of all, is it

[tex]\lambda = d \frac{a}{a^2+l^2}[/tex]

or

[tex]\lambda = d (\frac{a}{a^2} +l^2)[/tex]?

I suppose you mean the first one, but it is not clear. If you are not entering formulas as LaTeX you should at least use parentheses to make things unambiguous.

If you mean the first one, you solved for d correctly.

And please don't start a new thread when it makes sense to continue in the old one, it helps keep track of what is going on.

[chanelo]

OOPS, I meant the first one but it was supposed to be a divided by the SQUARE ROOT of a² + l²!

[Borek]

So for the record:

[tex]\lambda = d \frac{a}{\sqrt{a^2+l^2}}[/tex]

[curiouscat]

First of all, is it

[tex]\lambda = d \frac{a}{a^2+l^2}[/tex]

or

[tex]\lambda = d (\frac{a}{a^2} +l^2)[/tex]?

I suppose you mean the first one, but it is not clear.

Neither, probably. Both are dimensionly inconsistent. Assuming a, l, λ are all length-units. 

[chanelo]

Yes! That's the original equation, so I just flipped the λ with d and I put a on the bottom, with the square root of a² and l² on top to get an answer of 1131.67. Also, where do I go to make LaTeX formulas like what Borek has?

[Borek]

where do I go to make LaTeX formulas like what Borek has?

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