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This question is about using a diffraction grating to view the emission spectrum of sodium.

Light from a sodium discharge tube is incident normally upon a diffraction grating having 8.00 x 10^5 lines per meter. The spectrum contains a double yellow line of wavelengths 589 nm and 590 nm.

Determine the angular separation of the two lines when viewed in the second order spectrum.

For this question, I first used the resolvance equation R=average wavelength/difference in wavelength= m x N (mth order of diffraction, N number of slits or lines)

The answer is 0.2 degrees, please can anyone smart enough answer this extremely difficult question? This is from a high school physics textbook.

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  • $\begingroup$ Differentiate $m \lambda = d \sin \theta$ with respect to $\lambda$ noting that $m$ and $d$ are constant and $\Delta \theta$ is in radians. $\endgroup$
    – Farcher
    Apr 4, 2022 at 20:14

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Firstly, you can find the distance, $d$, between each of the holes through which the light diffracts from the number of lines per metre, $N$.

Then you can use the equation for a diffraction grating: $dsin(\theta)=m\lambda$

Where $m$ is the order of diffraction and $\lambda$ is your incident wavelengths. You can rearrange to find the angle, $\theta$, by which each incident wavelength will diffract.

Once you have the angles you can calculate the difference between them.

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    $\begingroup$ Welcome to PSE! You should read the help pages to understand what we do here. One thing we don't allow is complete answers to homework-like questions. We are not here to do people's homework, but to help with the physics behind the question. So please re-write your answer to address the physical principles involved. $\endgroup$
    – garyp
    Feb 16, 2021 at 12:47

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