± A Diffraction Grating Spectrometer Suppose that you have a reflection diffract

Question

± A Diffraction Grating Spectrometer Suppose that you have a reflection diffraction grating with n=135 lines per millimeter. Light from a sodium lamp passes through the grating and is diffracted onto a distant screen. Part A Two visible lines in the sodium spectrum have wavelengths 498nm and 569nm. What is the angular separation (change of theta) of the first maxima of these spectral lines generated by this diffraction grating? Express your answer in degrees to two significant figures. ± A Diffraction Grating Spectrometer Suppose that you have a reflection diffraction grating with n=135 lines per millimeter. Light from a sodium lamp passes through the grating and is diffracted onto a distant screen. Part A Two visible lines in the sodium spectrum have wavelengths 498nm and 569nm. What is the angular separation (change of theta) of the first maxima of these spectral lines generated by this diffraction grating? Express your answer in degrees to two significant figures. Suppose that you have a reflection diffraction grating with n=135 lines per millimeter. Light from a sodium lamp passes through the grating and is diffracted onto a distant screen. Part A Two visible lines in the sodium spectrum have wavelengths 498nm and 569nm. What is the angular separation (change of theta) of the first maxima of these spectral lines generated by this diffraction grating? Express your answer in degrees to two significant figures. Part A Two visible lines in the sodium spectrum have wavelengths 498nm and 569nm. What is the angular separation (change of theta) of the first maxima of these spectral lines generated by this diffraction grating? Express your answer in degrees to two significant figures.

Explanation / Answer

No.of lines per mm = 135 grating element d = 1/ 135 = 7.407*10^-3 mm d = 7.407*10^-6 m wavelengths λ = 498 * 10 ^-9 m λ ' = 569 * 10 ^-9 m condition for 1 st maximum d sinθ = λ from this sin θ = λ / d = 0.06723 θ = 3.854 degrees for wavelength λ ': ------------------ d sin θ ' = λ ' sin θ ' = λ ' / d = 0.0768 θ ' = 4.405 degrees So, angular separation = θ ' -θ= 0.55 degrees

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