A diffraction grating has a second-order resolving power of 1 250. (a) Find the number of illuminated lines on the grating. (b) Calculate the smallest difference in wavelengths surrounding 525 nm that can be resolved in the first-order diffraction pattern.
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So in this problem, it is given that the diffraction grating has the second order resolving power off 1250. So when Emma goes to our egos to all 50 All right. So for part A, we want to find the number off illuminated lines and the grating. So first of all, the resolving power for diffraction grating is given by our cause and M, and from here and which is the number of lines that are illuminated is going to be our over M. And this is going to be a tool 50 over two. And this will give me a 625. So number of lines does that are eliminated is 625. Okay, so this goto part B now for part B to find the smallest difference in Web link that is Delta Lambda surrounding the web link 525 which is seven and 25 nanometer. Okay, I will just write this down in meters 10 to the negative nine meters. So to find Delta Lambda that can be resolved in first order diffraction, we actually use our cause. Lambda over Delta Lambda. And remember this is the case off first order diffraction. So in this case, M is going to be one, right? This guy here is one. So that is actually going to give us Delta Lambda because Lambda over. And because, as I said, I am a close one, and this is going to give me 5 25 times 10 to the negative nine over 6 25 and this is actually a zero point eight for nanometer.