A diffraction grating with 500 lines per mm is held directly in front of the lens of a digital camera, with a bright white light source 8m away. The image recorded by the camera shows both the light source and the spectrum created by the light source. We know that the CMOS array of the camera has a pitch of 0.0036 mm per pixel, and the separation between the light source in the image and the middle of the "blue" region in the spectrum is about 730 pixels, which translates to a distance of 2.63mm. Based on this information, find the angle to the first order maximum of the blue light. Does this angle agree with the theory?
d = (1/500)mm
λ = 475 nm (for blue light)
The Attempt at a Solution
This gives a prediction of about 13 degrees for θ.
I'm not even sure what the relevant distances would be to get an angle from the picture. I've tried many permutations, and the closest I can get to 13 degrees is just 3 degrees. Does anyone have any idea how I can test the equation by using the picture?