Question #102516
A diffraction grating has 2000 lines. Two sources of monochromatic lights emanating wavelengths λ1 and λ2 are just resolved by the grating in the first order spectrum. If the mean of λ1 and λ2 is 600 nm, calculate the difference between the wavelengths
1
Expert's answer
2020-02-10T09:44:50-0500

R=mN=λ1λ2λ1R=mN=\dfrac{\lambda_1}{\lambda_2-\lambda_1} ​


λ1+λ22=600\frac{\lambda_1+\lambda_2}{2}=600 λ1=1200λ2\to\lambda_1=1200-\lambda_2


m=1m=1


So, we have

1200Nλ1Nλ1N=λ11200N-\lambda_1N-\lambda_1N=\lambda_1

1200N=λ1(2N+1)1200N=\lambda_1(2N+1)

from these two equations we get


λ1=1200N2N+1=1200200022000+1=599.85nm\lambda_1=\dfrac{1200N}{2N+1}=\dfrac{1200\cdot 2000}{2\cdot 2000+1}=599.85 nm

λ2=1200599.85=600.15nm\lambda_2=1200-599.85=600.15 nm


Hence the difference is

λ2λ1=600.15599.85=0.3nm\lambda_2-\lambda_1=600.15-599.85=0.3 nm



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