Light waves through grating. Min and Max measurements of wavelenghts in nm

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SUMMARY

The discussion centers on calculating the minimum and maximum wavelengths of light passing through a 220 lines/mm grating, observed on a screen 1.4m wide and 1.2m behind the grating. The relevant equations include y = L tan(Ø) and d sin(Ø) = m * wavelength. The user initially misinterpreted the line density and struggled with the calculations, leading to incorrect wavelength values. Correct understanding of the grating spacing (d) and proper application of the equations are crucial for accurate results.

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Homework Statement


Light passes through a 220 lines/mm grating and is observed on a 1.4m wide screen located 1.2m behind the grating. Three bright fringes are seen on both sides of the central maximum.

What are the minimum and maximum possible values of the wavelength?
Express your answers in nm.

Homework Equations


y=LtanØ
dsinØ=m*wavelength

The Attempt at a Solution



I started by looking at the first equation that is listed. y=LtanØ
To find y, I just looked at the 220lines/mm and that is .00022lines/nm. So then I just converted L into nm and plugged in the numbers.

700000000 = 1200000000tanØ
then
tan-1(700000000/1200000000) = about 30 degrees? ... I then put that into the second equation and get something wayyyy off for the wavelength. like .00037nm?
I've been working on this problem for over an hour and can't seem to find what I'm doing wrong or how to approach this the correct way. Any help is appriciated. Thanks!
 
Last edited:
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d is the distance between two lines in the grating (hint: it is not a density)
 

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