# Angular separation of the lines in a diffraction grating problem

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.

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

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.