हिंदी
Karnataka Board PUCPUC Science Class 11
पाठ्यपुस्तक उत्तर१२०७२
अवधारणा स्पष्टीकरण और वीडियो३१८
पाठ्यक्रम

Measurement of Length

Advertisements

Topics

  • Length and Its Measurement  
  • The Parallax Method
  • Activity: Understanding Parallax Through Experience
  • Measuring Stellar Distances
  • Measuring the Size od Celestial Objects
  • Measuring Very Small Distances
  • Special Units for Large Distances
  • Example
Maharashtra State Board: Class 11

Length and Its Measurement

Length is one of the fundamental quantities in physics - a basic building block we use to describe our physical world. The SI unit for length is the metre (m). 

Fun Fact: Originally, a metre was defined as one ten-millionth of the distance from the equator to the North Pole! Today's definition is much more precise. 

The Modern Definition of a Metre 

Since 1983, we have defined one metre as: "The distance light travels in a vacuum during 1/299,792,458 of a second". 

Because light always travels at the same speed in a vacuum - exactly 299,792,458 metres per second. This makes our measurement standard incredibly precise and the same everywhere in the universe! 

The Incredible Scale of Distances 

Our universe contains objects spanning an enormous range of sizes. Here's a journey from the largest to the smallest distances we can measure: 

From Galaxies to Atoms: A Scale of Distances

Object Distance/Size In Perspective
Andromeda Galaxy 2 × 10²² m Our nearest major galaxy neighbor
Proxima Centauri 4 × 10¹⁶ m Closest star after our Sun
Pluto 6 × 10¹² m Edge of our solar system
Earth's Radius 6 × 10⁶ m Our home planet
Mount Everest 9 × 10³ m Highest mountain on Earth
Paper Thickness 1 × 10⁻⁴ m About the width of a human hair
Virus Length 1 × 10⁻⁸ m Too small to see with regular microscopes
Hydrogen Atom 5 × 10⁻¹¹ m The smallest atom
Proton Radius 1 × 10⁻¹⁵ m Inside the atom's nucleus
Maharashtra State Board: Class 11

The Parallax Method

Measuring Astronomical Distances: The Parallax Method 

When measuring distances to stars and planets, we can't use a measuring tape! Instead, we use a clever technique called parallax. 

Maharashtra State Board: Class 11

Activity: Understanding Parallax Through Experience

Aim: The closer an object is, the more it appears to move when we change our viewing position.

Procedure:

  1. Hold your finger about 30 cm in front of your face.
  2. Close your left eye and note your finger's position against the background.
  3. Now close your right eye and open your left eye.
  4. Notice how your finger appears to "jump" against the background.
  5. This apparent movement is called parallax - the change in an object's apparent position when viewed from different locations.

Fig.1.2: Parallax method for determining distance.

Observations:

  1. Two Observation Points: We choose two locations on Earth separated by a distance b.
  2. Simultaneous Observation: Two observers watch the same planet at the same time.
  3. Measure the Angle: We measure the parallax angle θ between the two sight lines
  4. Calculate Distance: Using the formula: D = b/θ (where θ is in radians).

Fig.1.3: Measurement of distances of planets 

Conclusion: Since astronomical distances are enormous compared to Earth's size, the parallax angle θ is extremely small, making precise measurements challenging but possible with modern instruments.

Maharashtra State Board: Class 11

Measuring Stellar Distances

For stars, even using opposite sides of Earth isn't enough - the angles are too tiny to measure! 

The Solution: We use Earth's orbit around the Sun as our baseline: 

  • Baseline: 2 AU (astronomical units) - Earth's position 6 months apart
  • Measurement: Take photos of the same star 6 months apart
  • Calculation: Use the same parallax formula with this much larger baseline 
Maharashtra State Board: Class 11

Measuring the Size of Celestial Objects

Once we know a planet's distance, we can find its size using angular diameter: 

If a planet subtends an angle α at distance D, then: 
Planet diameter = α × D (where α is in radians)

Fig. 1.4: Measurement of size of a planet 

Maharashtra State Board: Class 11

Measuring Very Small Distances

For atomic-scale measurements, traditional tools won't work. We use: 

  • Electron Microscopes: Use electron waves instead of light waves
  • Tunneling Microscopes: Detect quantum effects at atomic scales
  • Wavelength Limitation: We can only see details smaller than the wavelength of our "light." 
Maharashtra State Board: Class 11

Special Units for Large Distances

Special Units for Large Distances 

Astronomers use convenient units for vast distances: 

  • Astronomical Unit (AU): 1.496 × 10¹¹ m (Earth-Sun distance)
  • Light-year: 9.467 × 10¹⁵ m (distance light travels in one year)
  • Parsec: 3.08 × 10¹⁶ m (distance where 1 AU subtends 1 arcsecond)

Memory Tip: "Parsec" comes from "parallax second" - the distance at which our solar system's diameter appears as 1 arcsecond! 

Maharashtra State Board: Class 11

Example

A star 5.5 light-years away shows a parallax of only 1.186 arcseconds when viewed from opposite sides of Earth's orbit - that's smaller than the angle of a coin seen from 4 kilometers away!

Test Yourself

Advertisements
Share
Notifications

Englishहिंदीमराठी
Login
Create free account


      Forgot password?
Course
Use app×