Question

The relation between $\theta $, b and D is:

(where $\theta $ is the parallax angle, b is the distance between two points of separation, D is the distance of source from any point of observation)
A. $\theta = \dfrac{b}{D}$
B. $\theta = \dfrac{D}{b}$
C. $\theta = b \times D$
D. $\theta = {b^2} \times D$

Answer 1

Hint To answer this question at first we should have been very much clear with the figure. From the figure we have to find the value of tan $\theta $. The expression for tan $\theta $ will give us the required answer to this question.

Complete step by step answer
Since we have to consult the figure for finding the relationship between $\theta $, b and D, let us first be familiar with this. So given below is the diagram:

As we know that we have to find the value for tan $\theta $, from the figure it is clear that:
$\tan \theta = \dfrac{b}{D}$.
Here as mentioned $\theta $ is the parallax angle, b is the distance between two points of separation, D is the distance of source from any point of observation.
We know that $\theta $ is a very small angle. So the value of tan $\theta $ will be very less as well. Therefore there will not be much difference between tan$\theta $ and $\theta $. So for our convenience we can assume that:
$\tan \theta \sim \theta $
So we get from the figure that:
$\theta = \dfrac{b}{D}$
So we can say that the relation between $\theta $, b and D is $\theta = \dfrac{b}{D}$.

Hence the correct answer is option A.

Note In the answer we have come across the term parallax angle. For better understanding we have to understand the meaning of this term. By parallax angle we mean the angle that is formed between the Earth at a specific time of the year and again the Earth, but this time it is only 6 months later.
From the parallax formula we get this idea that the distance of a star will be equal to 1 divided by that of the parallax angle. The parallax angle is measured in arc-seconds and the distance is measured in parsecs.