How Do You Calculate Unknown Wavelengths Using Diffraction Grating Formulas?

[Laceb04]

For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 26°. For an unknown wavelength, the same grating produces a bright fringe at an angle of 56°. In both cases the bright fringes are of the same order m. What is the unknown wavelength?
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Info: The Diffraction Grating & Compact Discs, Digital Video Discs, and the Use of Interference


My answers all keep coming out wrong. I don't know what I'm doing!

 

[quantumdude]

My answers all keep coming out wrong. I don't know what I'm doing!

It's hard for us to tell what you're doing wrong when you don't post your work. Let's see your attempted solution.

 

[runphysics]

According to the short cut formula
n lambda = d sin theta
just set up x sine angle to 420 sine angle ratio.
However, this only works for small angles.
If that does not give right answer, you have to distance ratios