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# A beam of $541-\mathrm{nm}$ light is incident on a diffraction grating that has 400 grooves $/ \mathrm{mm}$ (a) Determine the ang of the second-order ray. (b) What If? If the entire apparatus is immersed in water, what is the new second-order angle of diffraction? (c) Show that the two diffracted rays of parts (a) and (b) are related through the law of refraction.

## $=25 \cdot 6^{\circ}$

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### Video Transcript

the first thing you do in this problem is find our spacing between the greetings. So we have our d is determined by one millimeter, and there's 400 on grades in each millimeter, which means our distance is gonna be between each gray is gonna be 2500 nanometers. And so we're gonna have to find a second order. We're going to 2500 nanometers times Sign of my angle is gonna equal two times 5 41 So therefore, a sign of my angle. 0.43 to 8. And my angle would then be 25 0.645 degrees. Okay, uh, submersion, the whole thing underwater, uh, gets gives us an end value of 1.33 doesn't change the frequency of our lights. So therefore, it has to change the wavelength. So when do ah are original wavelength and divided? Our new wavelength is equal to end, and therefore my new wavelength is going to be equal to 406.77 In applying the same formulas, we're gonna have 2500 in time. Sign of data equals two times for a 6.77 Therefore scientific data. There's gonna be a 0.3 to 54 and therefore angle in this case, maybe around 18.99 degrees. Okay. Ah, last city. Should they're related through laws, the laws of refraction really signed of our first day that divided by a sign of our second beta. I should be equal to our index of refraction. Okay, It's a sign of our first data. Ah, was, ah. 0.43 to a inside of our second date of a 0.3 to 54 And thats approximately equal to 1.33 Okay, thank you very much.

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Kennesaw State University