Three thin prisms are combined as shown in figure (20-E1). The refractive indices of the crown glass for red, yellow and violet rays are μr, μy and μv respectively and
those for the flint glass are μ’r, μ’y and μ’v respectively. Find the ratio A’A for which A there is no net angular dispersion, and B there is no net deviation in the yellow ray.
Given that
The refractive indices of the crown glass for red, yellow and violet rays are μr, μy and μv respectively
for the flint glass are μ’r, μ’y and μ’v respectively
Now,
Total deviation for yellow ray produced by the prism combination is
δv-δr= δcy-δfy+δcy = 2δcy-δfy = 2(μcy-1)A-(μfy-1)A’
Similarly, the angular dispersion produced by the combination is
δv-δr= 2(μvc-1)A-(μvf-1)A’
A for net angular dispersion to be zero,
δv-δr = 0
2(μvc-1) A-(μvf-1) A’=0
2(μvc-1) A=(μvf-1) A’
B for net deviation in the yellow ray to be zero,
δy= 0
2(μcy-1) A-(μfy-1) A’=0
2(μcy-1) A=(μfy-1) A’
