Question

Speed of Light in vacuum is :

• A. $3 \times 10^6$ m/s
• B. $3 \times 10^8$ m/s
• C. $3 \times 10^5$ m/s
• D. $3 \times 10^7$ m/s

Hint:

A common mistake is choosing $3 \times 10^5 \text{ km/s}$. While that value is correct in kilometers, always check the units. In meters per second (m/s), which is the SI standard, the exponent must be $10^8$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the standard value of the universal physical constant \( c \), which represents the maximum speed at which all conventional matter and information in the universe can travel.
Step 2: Detailed Explanation:

Exact Value: The speed of light in a vacuum is exactly defined as $299,792,458$ meters per second. For calculation purposes in most physics problems, it is approximated to $3 \times 10^8 \text{ m/s}$.

Universal Constant: Light speed is constant in a vacuum regardless of the motion of the source or the observer, which is the foundational principle of Albert Einstein's Theory of Special Relativity.

Significance in Calculations: It is used in many fundamental equations, most famously \( E = mc^2 \), relating energy and mass. It also determines the "light-year," a unit of distance in astronomy.

Speed in Media: When light travels through other media (like water, glass, or air), it slows down. The ratio of the speed in vacuum to the speed in a medium is called the "refractive index" (\( n = c/v \)).

Magnitude Comparison: To visualize this speed, light can circle the entire Earth approximately 7.5 times in a single second. This illustrates why light speed appears "instantaneous" in daily terrestrial life.

Step 3: Final Answer:
The standard scientific value for the speed of light in a vacuum is $3 \times 10^8 \text{ m/s}$.

Answer 2

The value can also be pinned down by working backward from how fast light travels through a familiar medium and undoing the slowdown caused by that medium, using the refractive index relation \( n = \dfrac{c}{v} \), so \( c = n \cdot v \).

1. \(3 \times 10^6\) m/s: Water has a refractive index of about \(1.33\) and light is experimentally measured to travel through it at roughly \(2.25 \times 10^{8}\text{ m/s}\). Multiplying, \(c = 1.33 \times 2.25\times10^{8} \approx 3\times10^{8}\text{ m/s}\), a value far larger than this option offers, so it's incorrect.
2. \(3 \times 10^8\) m/s: This is exactly what the refractive-index calculation above yields, confirming the vacuum speed independently of the value used for visible light frequency and wavelength.
3. \(3 \times 10^5\) m/s: This is roughly a thousand times smaller than what the water-based calculation produces, ruling it out.
4. \(3 \times 10^7\) m/s: This is about ten times smaller than the value the refractive-index relation gives, so it also fails this cross-check.

Cross-checking through the physics of refraction in water lands on the same figure as the accepted vacuum value.

Therefore, the correct answer is \(3 \times 10^8\) m/s.