A dip needle lies initially in the magnetic meridian when it shows an angle of dip $\theta$ at a place. When the dip circle is rotated through an angle ${30}^o$ in the horizontal plane, the dip needle shows an angle of dip ${\theta }^1$. Then the value of $\frac{\tan {\theta }^1}{\tan \theta }$ is 

• A

  $\raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

• B

  2

• C

  $\sqrt{3}$

• D

  $2/\sqrt{3}$