Two magnets A and B are identical and these are arranged as shown in the figure. The (short magnets are considered) ratio of distance d1 and d2 will be,

The magnetic needle will align along the total magnetic field. In Equilibrium,  tanθ=BaxialBequatorial=B1B2 ⇒B1=B2tanθ  ⇒ μo4π 2Md13 = μo4π Md23tanθ⇒d1d2=2tanθ13=2cotθ13