A prism of angle A=60° has minimum deviation δ=30° with maximum experimental error 1°. If the permissible percentage error in refractive index μ is xπ/y %, find x+y.

Question

G1 Physics · Accepted Answer

At minimum deviation, μ=sin[(A+δ)/2]/sin(A/2)=sin45°/sin30°=√2. Only δ has stated error. Thus Δμ/μ≈(1/2)cot45°·Δδ=(1/2)(π/180)=π/360. Percentage error=100π/360=5π/18%. Hence x=5,y=18 and x+y=23.