Question regarding diffraction grating!

Question

anonymous · Answer

I am completely lost on this question -- if anyone could help me out, that would be greatly appreciated!
Thanks in advance

anonymous · Answer

@IrishBoy123 @Astrophysics @Michele_Laino @naveenbabbar

z4k4r1y4 · Answer

$$n=\frac{ d \sin \theta }{ \lambda }$$
where n= number of fringes, d=spacing between slits and $$\lambda=wavelength$$

anonymous · Answer

Here's my attempt,

Using Inference Equations for Bright Fringes:$$\huge y_\text{bright}=\frac{\lambda L}{d}m \implies m=\frac{y_\text{bright}d}{\lambda L}$$Given this, if we were to double the wavelength, then m would halve. If we were to double d, then m would double.

anonymous · Answer

@johnweldon1993 Does this seem correct? X) I know it's been a while since you've dealt with rays/light

johnweldon1993 · Answer

Ahh wth was that...umm...youngs equation? Idk i dont remember the name but those formulas you have DO seem familiar and from what i remember it makes sense!

anonymous · Answer

Yeah haha. The thing is, is that it keeps mentioning Young's Slits that deals with 2 or double slit gratings.. It doesn't specify how many gratings in my question =/

anonymous · Answer

Hmm, maybe the number of gratings doesn't matter here!

rvc · Answer

Well i dont remember much
i just remember he formula of difraction :/

anonymous · Answer

Yeah this chapter sucks haha. I hate light and optics..

So this is what I'm thinking..

In the question is says that m is the order of diffraction
Then it says m=x
Then # of Fringes = 2x+1

So,
a). If m halves by using the equations I posted, that means # of fringes = x+1
b). If m doubles, then # of fringes = 4x+1

I suppose that would be my answer? It feels like I should be answering it by saying that it doubles or halves... but it's asking for what happens to the number of fringes and it gives the relationship for that right there

rvc · Answer

relate it to the formula n try

anonymous · Answer

I thought I already did, though? I used the formula to tell whether m, the order of diffraction, doubles or halves. Then from there, I used the equation it gave me for the number of bright fringes. It also told me that x = m, so basically 

N = 2m + 1

in a), m is halved because the wavelength is doubled. So substituting (0.5m) for m, we get
N = m + 1

in b), m is doubled because the separation is doubled.
N = 4m + 1

Right?

rvc · Answer

i suppose u r correct
@Michele_Laino will confirm :)

michele_laino · Answer

I'm sorry, I'm not good with diffraction gratings! @rvc  @CShrix