The speed of light in vacuum is approximately:

Question

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The correct answer is Option A: $3 	imes 10^8 	ext{ m/s}$. The speed of light in a vacuum, universally denoted by the symbol $c$, is a fundamental physical constant. Its exact value is $299,792,458 ext{ m/s}$, which is standardly approximated as $3 imes 10^8 ext{ m/s}$ for scientific calculations. It represents the ultimate speed limit for the propagation of energy and information in the universe.

Step-by-Step Solution & Concepts:
The speed of light in a vacuum, universally denoted by the symbol $c$, is a fundamental physical constant. Its exact value is $299,792,458 ext{ m/s}$, which is standardly approximated as $3 imes 10^8 ext{ m/s}$ for scientific calculations. It represents the ultimate speed limit for the propagation of energy and information in the universe.

Working Principle: According to Maxwell's theory of electromagnetism, the speed of light in free space is determined by the electric permittivity ($\epsilon_0$) and magnetic permeability ($\mu_0$) of the vacuum. The mathematical relationship is expressed as $c = rac{1}{\sqrt{\mu_0 \epsilon_0}}$. In Einstein's Special Theory of Relativity, this speed remains constant for all observers regardless of their relative motion.

Key Formulas: $c = rac{1}{\sqrt{\mu_0 \epsilon_0}}$ — Relationship with vacuum permittivity and permeability; $c = f \lambda$ — Wave equation relating speed, frequency, and wavelength

Key Points: The standard approximated speed of light in a vacuum is $3 imes 10^8 ext{ m/s}$.; It is a fundamental universal constant utilized across physics and astronomy.; No particle with rest mass can attain or exceed this speed in a vacuum.

Applications: Definition of the meter in the International System of Units (SI); Astronomical distance measurements using light-years

Additional Info: Option A is the universally accepted standard approximation used in competitive exams.. Options B, C, and D contain incorrect powers of ten, representing wrong orders of magnitude.

Answer: A is correct — The speed of light in a vacuum is approximately $3 imes 10^8 ext{ m/s}$.

Exam Tip: Keep in mind that while light slows down when passing through dense media (like water or glass), its speed in a vacuum ($c$) always remains an absolute constant.

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Option B: $3 	imes 10^5 	ext{ m/s}$

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Option C: $3 	imes 10^6 	ext{ m/s}$

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Option D: $3 	imes 10^9 	ext{ m/s}$

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