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A diffraction grating have 4000 lines per cm is illuminated normally by light of wavelength 5000 $\mathring{A}$. Calculate its dispersive power in third order spectrum.

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1

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A diffraction grating have 4000 lines per cm is illuminated normally by light of wavelength 5000 $\mathring{A}$. Calculate its dispersive power in third order spectrum.

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written 6.2 years ago by | modified 6.2 years ago by |

N = 4000 line/cm, λ = 5000 x10$^{-8}$, n= 3

$ \frac{dθ}{dλ}= \frac{n}{(a+b)cosθ} \\[3ex] (a+b) sinθ = nλ \\[2ex] sinθ = \frac{nλ}{(a+b)} \\[2ex] sinθ = N nλ \,\,\,\,\,\ [\because (a+b) = \frac{1}{N}] \\[2ex] sinθ = 4000 \times 3 \times 5000 \times 10^{-8} = 0.6 \\[2ex] θ= 36.86 $

cosθ = 0.80

Therefore dispersive power $ \frac{dθ}{dλ} = \frac{Nn}{cosθ} = 15000 $

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