Diffraction - GRE Subject Test: Physics
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Question
A beam of light, with wavelength 
, is normally incident on a transmission diffraction grating. With respect to the incident beam, the first order diffraction maximum occurs at an angle of 
. What is the number of slits per centimeter on the grating?
A beam of light, with wavelength
Answer
The equation describing maxima of a diffraction grating is:
Where d is the separation of slits, which can also be expressed as:
Substituting d into the first equation and making the small angle approximation, one can solve for 
(lines per length):
Note that the angle had to be converted from degrees to radians. Finally, the question asks for lines per centimeter, not meter, so the answer becomes 
.
The equation describing maxima of a diffraction grating is:
Where d is the separation of slits, which can also be expressed as:
Substituting d into the first equation and making the small angle approximation, one can solve for
Note that the angle had to be converted from degrees to radians. Finally, the question asks for lines per centimeter, not meter, so the answer becomes
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