At an angle of ${30}^{\circ }$ to the magnetic meridian, the apparent dip is ${45}^{\circ }$. Find the true dip :

The correct option is D ${\tan }^{-1}\frac{\sqrt{3}}{2}$
Given:
Apparent dip, ${\varphi }_{ap}={45}^{\circ };\theta ={30}^{\circ }$
True dip, ${\varphi }_t=??$

We know that,

$\tan {\varphi }_{ap}=\frac{\tan {\varphi }_t}{\cos \theta }$

$\Rightarrow \tan {\varphi }_t=\tan {45}^{\circ }\times \cos {30}^{\circ }$

$\Rightarrow \tan {\varphi }_t=1\times \frac{\sqrt{3}}{2}$

$\therefore {\varphi }_t={\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Hence, option $\left(\text{D}\right)$ is correct.