Can the dispersive power ω=μv-μr be negative? What is the sign of ω if a hollow prism μ-1 is immersed into water?
No, dispersive power can never be negative because for a given medium, μ is a continuous function of wavelength.
In the equation,
μᵥ is always greater than μᵣ for the transparent prism kept in a medium having a lesser refractive index than it. So μᵥ-μᵣ > 0. Also μ > 1, so μ-1 >0. Hence the dispersive power ⍵ will be positive.
a. If a hollow prism is immersed in water the equation of the dispersive power will become
⍵ = ( - )/ -1
So both the numerator and the denominator will become negative and we will get ⍵ positive.
So in normal situations ⍵ will not be negative.
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