Measurement Of Length

The length may be defined as the distance of separation between two points in space.

There are two methods for the measurement of length.

1. Direct Method

In this method, measurement of length involves the uses of

(I) Meter scale (From 10⁻³ m to 10² m).

(II) Vernier callipers (Upto 10⁻⁴ m).

(III) Screw gauge or spherometer meter (upto 10⁻⁵ m).

2. Indirect Method

These methods are used to measure large distances such as the distance of a planet or a star from the Earth.

There are many indirect methods such as Echo method, Parallax method, LASER method, RADAR method etc.

Parallax Method

Parallax is the apparent shift in the position of an object with respect to another, when we shift our eye sidewise.

When we hold a pencil in front of us against some specific point on the background (a wall) and look at the pencil first through our left eye L (closing the right eye) and then by our right eyes R (closing the left eye), we find that position of pencil changes with respect to the wall. This is called parallax.

Parallax Angle
Parallax Angle

The distance between the left eye (L) and right eye (R) is the basis (b), so angle LOR=θ is called the parallax angle or parallactic angle. Since LR = b is very small as compared to the point distance O, i.e D. So, LR as an are of length b and radius LO=RO=D.

Parallax Angle
Parallax Angle

Knowing b and measuring θ in radians, we can calculate D. As b/D << 1, So parallax angle θ is too small to be measured.

Distance Of The Moon Or Any Planet (By Parallax Method)

To major the distances of the moon or a far away planet P, we observe it simultaneously from two observation A and B on the earth, separated by a large distance AB = b.

The distance between the two points of observation is called basis. Now, we select a distant star C whose position and direction can be taken approximately same from A and B.

Parallax Method
Parallax Method

Now angle PAC = θ₁ and angle PBC = θ₂ are measured from the two observations at the same time. As b<< S, So we can take AB as an arc of length b.


Parallax Method
Parallax Method

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