Light Diffraction Homework: 2 Wavelengths & Angle of Coincidence

[pat666]

Homework Statement

12 Light consisting of two wavelengths which differ by 160 nm passes through a diffraction grating with 2.50 x 10⁵ lines per metre. In the diffracted light, the third order of one wavelength coincides with the fourth of the other. What are the two wavelengths and at what angle of diffraction does this coincidence occur?

Homework Equations

y=n$$\lambda$$L/d I think is what I should be looking at??

The Attempt at a Solution

$$\Delta$$$$\lambda$$=160*10^-9
d=1/2.5*10^5 = 4*10^-6 not sure if this part is right
If my d is right I think that what I should do next is
y₃=3*$$\lambda$$*L/4*10^-6
y₄=4*$$\lambda$$*L/4*10^-6
these are both bright fringes but maybe one should be dark?
That is as far as I get at the moment!

Thanks for any help.

 

[rl.bhat]

Formula for diffraction grating is

d*sin(θ) = mλ

at the point of coincidence θ is same for both the wavelengths. So

m1λ1 = m2λ2

3*λ1 = 4(λ1- 160)

Solve for λ1. And then proceed to find the other results.

 

[pat666]

Thanks rl.bhat,
$$\lambda$$₁=6.4*10^-7m
$$\lambda$$₂=4.8*10^-7m
assuming my value for d from my 1st post is correct,
3*6.4*10^-7=4*10-6 sin ($$\theta$$)
$$\theta$$=28.69^o
Does this seem right, mainly concerned about my value for d??

Thanks

 

[rl.bhat]

You are right.