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Exercise:
The light of a HNe laser laO is diffracted on a grating with a grating constant of NO. The erference pattern is observed on a screen lO away from the grating. Calculate the position of the first three maxima with and without the small-angle approximation.

Solution:
The slit separation is given by the grating constant d dF The condition for maxima is sinalpha_m mfraclambdad mlambda N The position on the screen is a_m elltanalpha_m aF labeleq_full For m we find a_ ltimestanarcsinmtimeslatimes N a approx resultaP- For m and m the values are a_resultabP- and a_resultacP- With the small-angle approximation sinalphaapproxtanalpha refeq_full can be written as a_m &approx aapproxF For m we find a_ &approx ltimesmtimeslatimesN aapprox approx resultaapproxP- For m and m the results are a_approxresultabapproxP- and a_approxresultacapproxP-. For the first two maxima the approximated results agree with the results of the full solution within the given accuracy.
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Exercise:
The light of a HNe laser laO is diffracted on a grating with a grating constant of NO. The erference pattern is observed on a screen lO away from the grating. Calculate the position of the first three maxima with and without the small-angle approximation.

Solution:
The slit separation is given by the grating constant d dF The condition for maxima is sinalpha_m mfraclambdad mlambda N The position on the screen is a_m elltanalpha_m aF labeleq_full For m we find a_ ltimestanarcsinmtimeslatimes N a approx resultaP- For m and m the values are a_resultabP- and a_resultacP- With the small-angle approximation sinalphaapproxtanalpha refeq_full can be written as a_m &approx aapproxF For m we find a_ &approx ltimesmtimeslatimesN aapprox approx resultaapproxP- For m and m the results are a_approxresultabapproxP- and a_approxresultacapproxP-. For the first two maxima the approximated results agree with the results of the full solution within the given accuracy.
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Attributes & Decorations
Branches
Diffraction
Tags
double slit, interference
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration