Compute the following problem given below:

Problem: A diffraction grating is used to identify samples of chemical elements by their line spectra. For Lithium (Li), there are three very close lines that form a single line at 610 nm.

Part I: Calculate the slit separation distance d needed to make this line appear at an angle of 20.0°. What color is this line?

Part II: Lithium has another strong line at 671 nm. At what angle will this line appear? What color is this line?

Part III: The next strongest Lithium line is at 812.6 nm, which is in the infrared and can't be seen well with your eye. Discuss how you might detect this radiation.

Please explain each step and equations used to get the solution.