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?

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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 .

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