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 :

• A. ${\tan }^{-1}\left(\tan \delta \right)$
• B. ${\tan }^{-1}\left(\tan \delta \cos \theta \right)$
• C. ${\tan }^{-1}\left(\tan \delta \sec \theta \right)$
• D. $0$

Answer 1

Answer: (C)

${\tan }^{-1}\left(\tan \delta \sec \theta \right)$

Let ${\delta }_1$ be the angle of dip when dip circle is in magnetic meridian
$\tan {\delta }_1=\frac{V}{H}$
The dip circle when makes an angle $\theta$ , horizontal component of the earth's magnetic field is $Hcos\theta$
The angle of dip when the dip circle makes an angle with the magnetic meridian is
$\tan {\delta }_1=\frac{V}{H\cos \theta }$
This is called apparent dip.
$\tan {\delta }_1=\frac{\tan \delta }{\cos \theta }$
${\delta }_1={\tan }^{-1}\left(\tan \delta \sec \theta \right)$