Angular Distance Between Mercury Doublet Images · RMPH 2018 #A2
Physics · optics
Problem
The prism with θ determined above and the direction of the incident beam remain fixed, but the nature of the light radiation changes, being formed now of the yellow doublet of the mercury. The two wavelengths have the values 579.1 nm, respectively 577 nm. The refraction indices of the glass for these wavelengths are n=1.60, respectively n+Δn, where Δn=1.3×10−4. The light rays that exit the prism enter longitudinally into an astronomical telescope adjusted for infinite distance.
Derive the mathematical expression for "the angular distance" Δβ between the two images seen through the telescope (first as a function of θ and Δn, then as a function of n and Δn) and calculate its numerical value.