7.
The visible spectrum has wavelength in the range of 400 nm to 700 nm. The angular
spread of the first-order visible spectrum produced by a plane diffraction grating having
6000 lines cm-, when the light is incident normal to the grating is
(a) 8.9°
(b) 9.9°
(c) 10.9°
(d) 11.9°
(e) 12.9°
Answers
Answer:
The first-order spectrum corresponds to m=1
. The grating has 600 lines per millimeter, so the grating spacing (the distance d between adjacent lines) is
d=1 mm600=1.67×10−6 m
With m=1
, the angular deviation of the violet light θv
, is given by
sinθv=mλd=(1)(4.00×10−7 m)(1.67×10−6 m)=0.240
So that θv=13.9∘
The angular deviation of the red light is given by
sinθr=(1)(7.00×10−7 m)(1.67×10−6 m)=0.420
Thus, θr=24.8∘
Therefore, the angular width of the first-order visible spectrum is 24.8∘−13.9∘=10.9∘
Conclusion: Increasing the number of lines per millimeter in the grating increases the angular width of the spectrum, but the grating spacing d
can?t be less than the wavelengths of the spectrum being observed. Do you see why?
Problem:
If the angular width of the first-order visible spectrum is instead 16.7∘−9.4∘=7.2∘
, how many lines per millimeter are there in the grating?
Diffraction Gratings:
Diffraction gratings are devices that are used in many advanced optical experiments. As opposed to single slit or double slit diffraction experiments, the fringes that diffraction gratings can produce are very much sharper than those few slits. The diffraction angles are very much the same as that of what we expect from double slits, so the equation to calculate these angles are given as:
dsinθ=nλ
where:
d is the slit separation distance
θ
is the diffraction angle
n is the fringe order number (whole numbers for bright, half-integers for dark)
λ
is the incident light wavelength
Explanation:
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Explanation:
Calculate how much lines are there per meter and convert the wave lengths to meters too... Use the equation:
sin a = (n × lambda ) / d