Answer to Question #164079 in Optics for SAmanta Ariel

Question #164079


          A diffraction grating has 1.2 × 104 rulings or lines uniformly spaced over a width w = 25.4mm. This grating is illuminated at normal incidence by yellow light from a sodium vapour lamp of wavelength 589nm. Determine the greatest angle at which an order can occur on either side of the center of the diffraction pattern?


1
Expert's answer
2021-02-17T12:07:27-0500

The grafting spacing d is,

d=wNd= \dfrac{w}{N} =25.4×1031.2×104=21.167×107m=2117nm= \dfrac{25.4\times 10^{-3}}{1.2\times10^4}=21.167 \times 10^{-7}m = 2117nm

For diffraction pattern on either side of center n \geq 1

For λ\lambda = 589nm We have,

dsinθdsin\theta = nλ\lambda

θ=sin1(nλd)\rightarrow \theta = sin^{-1}(\dfrac{n\lambda}{d})

sin1(1×589×1092117×109)\rightarrow sin^{-1}(\dfrac{1\times589\times10^{-9}}{2117\times10^{-9}})

sin1(0.278)\rightarrow sin^{-1}(0.278) = 16.14°\degree

∴Ang \geq θ≈16.14°\degree


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