± A Diffraction Grating Spectrometer Suppose that you have a reflection diffract
ID: 2108148 • Letter: #
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 498 nm and 569nm. What is the angular separation (change in theta) of the first maxima of these spectral lines generated by this diffraction grating? Express your answer in degrees to two significant figures.Part B How wide does this grating need to be to allow you to resolve the two lines 589.00 and 589.59 nanometers, which are a well known pair of lines for sodium, in the second order (m=2)? Express your answer in millimeters 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 498 nm and 569nm. What is the angular separation (change in theta) of the first maxima of these spectral lines generated by this diffraction grating? Express your answer in degrees to two significant figures.
Part B How wide does this grating need to be to allow you to resolve the two lines 589.00 and 589.59 nanometers, which are a well known pair of lines for sodium, in the second order (m=2)? Express your answer in millimeters 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 498 nm and 569nm. What is the angular separation (change in theta) of the first maxima of these spectral lines generated by this diffraction grating? Express your answer in degrees to two significant figures.
Part B How wide does this grating need to be to allow you to resolve the two lines 589.00 and 589.59 nanometers, which are a well known pair of lines for sodium, in the second order (m=2)? Express your answer in millimeters to two significant figures. Part A Two visible lines in the sodium spectrum have wavelengths 498 nm and 569nm. What is the angular separation (change in theta) of the first maxima of these spectral lines generated by this diffraction grating? Express your answer in degrees to two significant figures.
Part B How wide does this grating need to be to allow you to resolve the two lines 589.00 and 589.59 nanometers, which are a well known pair of lines for sodium, in the second order (m=2)? Express your answer in millimeters to two significant figures. Part B How wide does this grating need to be to allow you to resolve the two lines 589.00 and 589.59 nanometers, which are a well known pair of lines for sodium, in the second order (m=2)? Express your answer in millimeters to two significant figures.
Explanation / Answer
Resolvance R = λ/Δλ ~= 1000.
Also R = mN, where m is the order and N is the number of slits.
Thus mN = 1000, and since m = 2, N = 500.
So width = 500/135 mm = 3.703 mm.
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