Problem involving interference and medium with index n

[LCSphysicist]

Homework Statement

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Relevant Equations

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> A diffraction grating, ruled with 300 lines per mm, is illuminated with a white light source at normal incidence. (ii) Water (of refractive index 1.33) now fills the whole space between the grating and the screen? What is the angular separation, in the first-order spectrum, between the 400 nm and 600 nm lines? [5]Second the solution of the question, the equation of máximum localization is now $d sin(\theta)/n = m \lambda$. The argument given to achieve this equation was that "the indicent plane light will suffers refraction between the two medium, such that $sin(\theta i) = n sin (\theta w)$.

Even so i can see a logic behind this argument, i am not totally convinced with the solution of it. I mean, i am not sure of that. Honestly, i think the author is using the incident angle to measure the angular separation, and i desagree. The wave will propagate parallel to the refracted angle $\theta w$, so the incident angle does not matter anymore. In this case, i would say that

**We could argue that the wavelength now is $\lambda/n$. Now since the angle that matters is, in fact, the angle after the slits, already in the medium, the equation should be $d sin(\theta w) = m \lambda /n$**.

THe problem with this solutions is that, if we substitute (Since i think both equations are essentially true, just differing the meaning of angular separation) $\theta w$ (my solution) and $\theta i$ (authors solution) in $sin(\theta i) = n sin (\theta w)$, we did'nt got $1=1$.

So one of the solutios is wrong. Probably mine, but i am not sure why.

 

[Doc Al]

**We could argue that the wavelength now is $\lambda/n$. Now since the angle that matters is, in fact, the angle after the slits, already in the medium, the equation should be $d sin(\theta w) = m \lambda /n$**.

That looks good to me.

THe problem with this solutions is that, if we substitute (Since i think both equations are essentially true, just differing the meaning of angular separation) θw (my solution) and θi (authors solution) in sin(θi)=nsin(θw), we did'nt got 1=1.

I fail to see what refraction has to do with this problem.