How many lines per centimeter does the grating have?

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SUMMARY

The discussion centers on calculating the number of lines per centimeter on a diffraction grating given a wavelength of 488 nm and a second-order bright fringe angle of 8.02°. The correct formula to use is d sin θ = nλ, where d is the grating spacing, n is the order of the fringe, and λ is the wavelength. The initial calculation of d was incorrect due to improper unit conversion, leading to an erroneous final result for the number of lines per centimeter. The correct approach requires converting the wavelength from nanometers to meters before performing the calculations.

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  • Understanding of diffraction grating principles
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  • Knowledge of unit conversion (nanometers to meters)
  • Basic trigonometry for angle calculations
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George_H
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Homework Statement



The light shining on a diffraction grating has a wavelength of 488 nm (in vacuum). The grating produces a second-order bright fringe whose position is defined by an angle of 8.02°. How many lines per centimeter does the grating have?


Homework Equations



d sin q = nl

The Attempt at a Solution



d = (2)(488)/sin(8.02) = 6995.474955

d = 1/N

N = 1/d = 1/6995.474955 =1.429495505X10^-4 (per M) X 100 = 0.014294955

It got this answer and it is wrong, I have no idea where to go from here or what to do and would be grateful of any help, thanks!
 
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You should convert the wavelength from nanometers to meters (or cm, whatever). I don't think you did that properly.
 
Last edited:

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