N = 4000 line/cm, λ = 5000 x10$^{-8}$, n= 3

$ \frac{dθ}{dλ}= \frac{n}{(a+b)cosθ} \\[3ex] (a+b) sinθ = nλ \\[2ex] sinθ = \frac{nλ}{(a+b)} \\[2ex] sinθ = N nλ \,\,\,\,\,\ [\because (a+b) = \frac{1}{N}] \\[2ex] sinθ = 4000 \times 3 \times 5000 \times 10^{-8} = 0.6 \\[2ex] θ= 36.86 $

cosθ = 0.80

Therefore dispersive power $ \frac{dθ}{dλ} = \frac{Nn}{cosθ} = 15000 $