Third-order maxima separation for 630 nm and 705 nm through diffraction grating

[tg22542]

Homework Statement

A grating has 1070 lines per centimetre, and a flat screen is perpendicular to the ray that makes the central peak of the diffraction pattern. The screen is 3.20 m from the grating. If light of two wavelengths, 630 nm and 705 nm, passes through the grating, what is the separation on the screen between the third-order maxima for the two wavelengths?

Homework Equations

mλ = dsinΘ

The Attempt at a Solution

d = 1/1070 = .000935 * 10 000 000 = 9345.79nm

λ1 = Θ1 = sin^-1(3*705 / 9345.79) = 13.0796°
λ2 = Θ2 = sin^-1(3*630 / 9345.79) = 11.6674°

[3.2tan(13.0796°)] - [3.2tan(11.6674)] = .082673 * 1000 = 82.67 nm


My answer is incorrect, can anyone see where I'm going wrong here?

Also, where I multiplied my numerator by 3 above, I did that due to the third order maxima, is that correct? I was impatient and also tried multiplying it by 2 instead, also incorrect.

Please help me out here.

 

[Doc Al]

A grating has 1070 lines per centimetre,

Check your arithmetic.

 

[tg22542]

oops.

Then shouldn't using (1/107) * 10000000 as my new value be right?

It's still wrong.

 

[Doc Al]

Then shouldn't using (1/107) * 10000000 as my new value be right?

It's still wrong.

Two things:
(1) That should be (.1/1070)
(2) 1 nm = 10^-9 m

 

[tg22542]

I still got it wrong.

I'll show you once more what I'm doing nowd = .1/1070 = .000093 * 10 000 000 = 934.579nm

λ1 = Θ1 = sin^-1(3*705 / 934.579) = x1°
λ2 = Θ2 = sin^-1(3*630 / 934.579) = x2°

[3.2tan(x1°)] - [3.2tan(x2)] = z

z*1000 = ansstill wrong thoughWhere exactly do i need to make changes, and what are those changes? I have 6 tries left.

 

[Doc Al]

I still got it wrong.

I'll show you once more what I'm doing nowd = .1/1070 = .000093 * 10 000 000 = 934.579nm

.1/1070 = 0.0000934579 m. So far, so good.
Why do you then multiply by 10 000 000? Instead, multiply by 10⁹.

 

[tg22542]

im doing all of this and still getting it wrong

 

[Doc Al]

im doing all of this and still getting it wrong

Post each step, just like you did before.

 

[tg22542]

Most previous try:

d = .1/1070 = .000093 * 10^9 = 93457.9 nm

λ1 = Θ1 = sin^-1(3*705 / 93457.9) = 1.297°
λ2 = Θ2 = sin^-1(3*630 / 93457.9) = 1.159°

[3.2tan(1.297)] - [3.2tan(1.159)]

= .0077 nm

 

[Doc Al]

Most previous try:

d = .1/1070 = .000093 * 10^9 = 93457.9 nm

λ1 = Θ1 = sin^-1(3*705 / 93457.9) = 1.297°
λ2 = Θ2 = sin^-1(3*630 / 93457.9) = 1.159°

[3.2tan(1.297)] - [3.2tan(1.159)]

= .0077 nm

That answer in is meters, not nm. What units do they want the answer in? mm makes sense.

 

[tg22542]

Well the units don't matter, hold on I will convert it and give it a try!

 

[tg22542]

7.7mm didn't work

 

[Doc Al]

7.7mm didn't work

I don't see an obvious error, unless it's just a significant figures issues. Often those systems want 3 sig figs no matter what.

Otherwise I will look at this more carefully later and see if there's another error that I missed.

 

[tg22542]

Sounds great. Thank you very much for your help this far.

 

[Doc Al]

Sounds great. Thank you very much for your help this far.

I don't see any errors in the calculation.

Did you try using 3 sig figs in your response? (I assume this is some online system, not a textbook problem, right?)

If all else fails, it might help to take a screenshot of the question so that we can check that there's no ambiguity. (Though it seems pretty clear.)

 

[tg22542]

I did try 3 sig figs.. still wrong. In my angle calculation (second step), I multiplied each wavelength by 3, is that correct?

 

[Doc Al]

In my angle calculation (second step), I multiplied each wavelength by 3, is that correct?

Sure.