Question

The angle of dip at a place is $\delta$. If the dip is measured in a plane making an angle $\theta$ with the magnetic meridian, the apparent angle of dip ${\delta }_1$ will be :

Answer 1

Step 1: Given

Dip angle = $\delta$

Angle with the magnetic meridian = $\theta$

Apparent angle of Dip = ${\delta }_1$

Step 2: Define the true angle of dip

The true angle of dip can be calculated as:

$\tan \delta =\frac{V}{H}$ (Where V and H are the vertical and horizontal components of the earth's magnetic field.)

Step 3: Define the apparent angle of dip

The apparent angle of dip when the plane is making an angle $\theta$ with the magnetic meridian is given by:

$$\begin{gathered} \tan {\delta }_1=\frac{V}{H\cos \theta } \\ =\frac{\tan \delta }{\cos \theta } \\ {\delta }_1={\tan }^{-1}\left(\frac{\tan \delta }{\cos \theta }\right) \\ ={\tan }^{-1}(\tan \delta sec\theta ) \end{gathered}$$

Therefore, the apparent angle of dip ${\delta }_1$ will be ${\tan }^{-1}(\tan \delta sec\theta )$.