( μv + μr )/2 is mean refractive index for prism and it is approximately taken as μy .
( μ is refractive index , subscripts v, r and y stands for violet, red and yellow colour respectively )
Dispersive power ω of prism is defined as, ω = ( δv - δr ) / δ ...............(1)
where δv is angular deviation for violet colour and δr is angular deviation for red colour.
δ is mean deviation, that is considered as deviation of yellow colour
since deviation δ = (μ-1)A , where μ is the refractive index of material of prism and A is angle of prism,
Eqn.(1) is written using the respective refractive indices as , ω = ( μv - μr )/ ( μy - 1) .............(2)
In eqn.(2) mean deviation is considered as deviation due to yellow colour.
while solving problems related to dispersion in glass prism, if μy is not given, we take arithmetic mean of μv and μr for
mean refractive index and find the dispersive power.
For given dispersive power, if we need to find μy using the given values of μv and μr , then we should use the equation (2)