Back to Directory
NEET PHYSICSMedium

If θ1\theta_1 and θ2\theta_2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ\theta is given by:

A

cot⁡2θ=cot⁡2θ1+cot⁡2θ2\cot^2 \theta = \cot^2 \theta_1 + \cot^2 \theta_2

B

tan⁡2θ=tan⁡2θ1+tan⁡2θ2\tan^2 \theta = \tan^2 \theta_1 + \tan^2 \theta_2

C

cot⁡2θ=cot⁡2θ1−tan⁡2θ2\cot^2 \theta = \cot^2 \theta_1 - \tan^2 \theta_2

D

tan⁡2θ=tan⁡2θ1−tan⁡2θ2\tan^2 \theta = \tan^2 \theta_1 - \tan^2 \theta_2

Step-by-Step Solution

  1. True Dip (θ\theta): The true angle of dip is related to the vertical component (VV) and horizontal component (HH) of Earth's magnetic field in the magnetic meridian by tan⁡θ=VH\tan \theta = \frac{V}{H} or cot⁡θ=HV\cot \theta = \frac{H}{V}.
  2. Apparent Dip: In a vertical plane making an angle α\alpha with the magnetic meridian, the effective horizontal component is H′=Hcos⁡αH' = H \cos \alpha, while the vertical component VV remains the same. The apparent dip θ1\theta_1 is given by: tan⁡θ1=VHcos⁡α⇒cot⁡θ1=Hcos⁡αV=cot⁡θcos⁡α\tan \theta_1 = \frac{V}{H \cos \alpha} \Rightarrow \cot \theta_1 = \frac{H \cos \alpha}{V} = \cot \theta \cos \alpha cos⁡α=cot⁡θ1cot⁡θ\cos \alpha = \frac{\cot \theta_1}{\cot \theta}
  3. Second Plane: Since the second plane is perpendicular to the first, it makes an angle (90∘−α)(90^\circ - \alpha) with the meridian. The apparent dip θ2\theta_2 is: tan⁡θ2=VHcos⁡(90∘−α)=VHsin⁡α⇒cot⁡θ2=Hsin⁡αV=cot⁡θsin⁡α\tan \theta_2 = \frac{V}{H \cos(90^\circ - \alpha)} = \frac{V}{H \sin \alpha} \Rightarrow \cot \theta_2 = \frac{H \sin \alpha}{V} = \cot \theta \sin \alpha sin⁡α=cot⁡θ2cot⁡θ\sin \alpha = \frac{\cot \theta_2}{\cot \theta}
  4. Derivation: Using the identity sin⁡2α+cos⁡2α=1\sin^2 \alpha + \cos^2 \alpha = 1: (cot⁡θ2cot⁡θ)2+(cot⁡θ1cot⁡θ)2=1\left( \frac{\cot \theta_2}{\cot \theta} \right)^2 + \left( \frac{\cot \theta_1}{\cot \theta} \right)^2 = 1 cot⁡2θ2+cot⁡2θ1cot⁡2θ=1\frac{\cot^2 \theta_2 + \cot^2 \theta_1}{\cot^2 \theta} = 1 cot⁡2θ=cot⁡2θ1+cot⁡2θ2\cot^2 \theta = \cot^2 \theta_1 + \cot^2 \theta_2
Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started
Solved: PHYSICS Question for NEET | Sushrut