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  4. The sodium yellow doublet has wavelengths 5890 Å and λ Å and resolving power of a grating to resolve these lines is 982 , then value of λ is

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Q. The sodium yellow doublet has wavelengths $5890 \, Å$ and $\lambda \, Å$ and resolving power of a grating to resolve these lines is $982$ , then value of $\lambda $ is

NTA AbhyasNTA Abhyas 2020Wave Optics

Solution:

Mean wavelength $\lambda _{m}=\frac{5890 + \lambda }{2}$
Wavelength difference $d\lambda =\lambda -5890$
Resolving power $R$ of a grating
$R=\frac{\lambda _{m}}{d \lambda }=\frac{\frac{5890 + \lambda }{2}}{\lambda - 5890}=982$
$\lambda =5896 \, Å$