Question

A dip needle shows an angle of dip $\theta$ in a place which is in the magnetic meridian. Now, the dip circle is rotated through an angle $x$ in the horizontal plane and then it shows an angle of dip ${\theta }_1.$ Value of $\tan {\theta }_1/\tan \theta$ is :

• A. $\frac{1}{\cos x}$
• B. $\frac{1}{\sin x}$
• C. $\frac{1}{\tan x}$
• D. $\cos x$

Answer 1

The correct option is A $\frac{1}{\cos x}$

assume horizontal component of field in magnetic meridian is $H$ and vertical component of magnetic field is $V$
If the dip circle makes an angle $x$ with the magnetic meridian , apparent horizontal component of field $H_a=H\cos x$
$\tan {\theta }_1=\frac{V}{H_a}$
${\theta }_1$ is the new dip angle (apparent dip angle)
$\tan {\theta }_1=\frac{V}{H\cos x}$
$\tan \theta =\frac{V}{H}$ , $\theta$ is the true dip angle
$\tan {\theta }_1=\sec x\times \tan \theta$