Question #162548

Parallel light consisting of 2 monochromatic radiations of wavelengths 6.0 x 10^(-5) cm and 4.0 x 10^(-5) cm falls normally on a plane transmission grating ruled with 5000 lines per cm. What is the angular separation of the second-order spectra of the two wavelengths?


1
Expert's answer
2021-03-05T07:27:44-0500

Given,

Wavelengths are (λ1)=6.0×105cm(\lambda_1)=6.0\times10^{-5} cm


λ2=4.0×105cm\lambda_2=4.0\times10^{-5} cm

Grating rule nd=5000\frac{n}{d}=5000 lines per cm


sinθ=nΔλd\Rightarrow \sin\theta= \frac{n\Delta \lambda}{d}


sinθ=5000×λ2λ1\Rightarrow \sin\theta = 5000\times \lambda_2-\lambda_1

=5000×(6×1054×105)=5000\times(6\times 10^{-5}-4\times 10^{-5})

=5000×2×105=5000\times 2\times 10^{-5}

=0.5=0.5

sinθ=12=sin30\sin\theta = \frac{1}{2}=\sin 30^\circ


Hence, θ=30\theta = 30^\circ

Hence, the required angular separation be 3030^\circ


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