Angular separation of the lines in a diffraction grating problem

Question

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.

Answer 1

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.