Diffraction grating wavelengths question

[ombudsmansect]

Hey guys this is the problem i need to solve:

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?


Attempt:

Ok I am assuming the question is saying that 3 wavelengths of one type of light is the same length of 4 wavelengths of the other, and that these coinciding on a screen of some sort will give point of maximum constructive interference (bright spot). SO using this information and the fact that the wavelengths differ by 160nm I am trying to figure out a set of equations to solve this. its not a lack of equations but ill have to set up some simultaneous equations probabl to solve through this. So ifff naybodys interested and a solution jumps out at those who might like solving this sort of gear your help is appreciated as this Q is annoyin me :)

 

[ombudsmansect]

ok i assumed that wavelength of light of the third order was longer than that of the 4th order one so:

L_1 - L_2 = 160nm

and from nL= dsintheta


3L_1 = dsintheta

divided by

4L_2 = dsintheta

using all of this info i got L_2 = 480nm, L_1 = 640nm

now subbed back in any of these two wavelengths into nL = sintheta

and got theta = 28.69 degrees

if there anyone readin this that might be able to give me a thumbs up on my procedure it would be greatly appreciated