Question #164552

A beam of parallel light is incident normally on a diffraction grating having 550 lines per mm. A

 telescope is used to observe the second order in the spectrum. Calculate the angular separation in radians of two spectra lines of wavelengths 559nm and 563nm.


1
Expert's answer
2021-03-14T19:47:30-0400

Here,

λ=559 nmλ+Δλ=563 nm\lambda=559\ nm\\\lambda+\Delta \lambda=563\ nm

Δλ=(563559)nm=4 nm\Delta \lambda=(563-559)nm=4\ nm

m=1d=1/550 =2×106mm=1\\d=1/550\ =2\times 10^{-6}m

 Now,

sinα1= mλ1/d

sinα2= mλ2/d

Substracting the two gives:

sinα1- sinα2= m(λ12)/d

Since the angles are small, we approximate sinα≈α to get the separation:

Angular separation α1α2=m(λ1λ2)d\alpha_1- \alpha_2=\dfrac{m(\lambda_1-\lambda_2)}{d}

=1(563559)×1092×106=2×103= \dfrac{1(563-559)\times 10^{-9}} {2\times 10^{-6}}=2\times 10^{-3}




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