How Do You Calculate Unknown Wavelengths Using Diffraction Grating Formulas?

Laceb04
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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!
 
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Laceb04 said:
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.
 
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
 

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