A magnetic needle can freely rotate in a vertical plane that makes an angle of 60^ with the magnetic meridian. If the needle settles in a direction making an angle of ⁻¹ ( 2 3 ) with the horizontal, determine the true dip at this location.

Step-by-step solution

Let the true dip be and the apparent dip be ' . The relation between true dip and apparent dip in a plane making an angle with the magnetic meridian is given by ' = Given ' = ⁻¹ ( 2 3 ) , we have ' = 2 3 . The angle with the magnetic meridian is = 60^ , so = 1 2 . Substituting these values into the formula, we get 2 3 = 1/2 = 2 3 1 2 = 1 3 = 30^