Answer to Question #164552 in Optics for Theodore

Question

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.

Answer 1

Here,

$\lambda=559\ nm\\\lambda+\Delta \lambda=563\ nm$

$\Delta \lambda=(563-559)nm=4\ nm$

$m=1\\d=1/550\ =2\times 10^{-6}m$

 Now,

sinα₁= mλ₁/d

sinα₂= mλ₂/d

Substracting the two gives:

sinα₁- sinα₂= m(λ₁-λ₂)/d

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

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

$= \dfrac{1(563-559)\times 10^{-9}} {2\times 10^{-6}}=2\times 10^{-3}$