Calculating Spectrum Width of White Light on a Diffraction Grating

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SUMMARY

The discussion focuses on calculating the spectrum width of white light using a diffraction grating with 3000 lines/cm. The relevant formula is the diffraction grating equation, nλ = d sin θ, where n is the order of the spectrum, λ is the wavelength, and d is the grating spacing. For this scenario, the longest wavelength (750 nm) corresponds to the second order (n=2) and the shortest wavelength (400 nm) corresponds to the third order (n=3). By applying trigonometric principles and the distance of 100 cm from the grating to the screen, the width of the spectrum can be determined.

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Velocity
This question really has me stumped..i would appreciate it if anyone could help me out:smile:

White light containing wavelengths of 400nm to 750 nm is shone normally onto a diffraction grating of 3000 lines/cm. Calculate the width of the spectrum that appears as the second antinode on a screen that is 100 cm away.

Is there a specific formula I can use to solve the question? If so then please help.. thanks
 
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Yes, use the diffractin grating equation.

n lamda = d sin theta

Rearrange the terms, solve for theta for two cases -- the longest wavelength at the n=2-mode and the shortest wavelength at the n=3-mode. Use this information with the distance between the grating and the screen to solve the problem -- just a little trigonometry.

eNtRopY
 

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