Question

A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit, if light takes 8 minutes and 20 seconds to cover this distance?
1. 820 units
2. 500 units
3. 1500 units
4. 2460 units

Answer 1

Correct Answer - Option 2 : 500 units

The correct answer is 500 units.

• Calculation: 
  • Given that the speed of light in a vacuum is unity.
    • Speed of light = 1 unit
  • Time taken = t = 8 min 20 s
    • \(8 × 60 + 20 = 480 + 20 = 500 s\)
  • Distance between the Sun and the Earth is given by= Speed of light × Time taken by light to cover the distance.
    • Distance between the Sun and the Earth = 1 × 500
    • so, Distance between the Sun and the Earth = 500 units

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• The wavelength of light:
  • It can be defined as the distance between two successive crests or troughs of a wave.
  • The wavelength of UV radiation is shorter than violet light.
  • Similarly, the wavelength of infrared radiation is longer than the wavelength of red light. 
  • Wavelength is inversely proportional to frequency.
• In the case of electromagnetic radiation such as light in free space, the phase speed is the speed of light, about 3×108 m/s.