The refractive index of a medium is 1.5. Calculate the speed of light in that medium (Speed of light in vacuum

Question

The refractive index of a medium is 1.5. Calculate the speed of light in that medium (Speed of light in vacuum = 3 	imes 10^8 m/s).

Examoogle · Accepted Answer

The correct answer is Option A: 2 	imes 10^8 	ext{ m/s}. The refractive index ($n$) of a medium is defined as the ratio of the speed of light in a vacuum ($c$) to the speed of light in that medium ($v$). Given $n = 1.5$ and $c = 3 	imes 10^8 	ext{ m/s}$, the speed in the medium is calculated as $v = \frac{c}{n} = \frac{3 	imes 10^8}{1.5} = 2 	imes 10^8 	ext{ m/s}$.

Step-by-Step Solution & Concepts:
The refractive index ($n$) of a medium is defined as the ratio of the speed of light in a vacuum ($c$) to the speed of light in that medium ($v$). Given $n = 1.5$ and $c = 3 	imes 10^8 	ext{ m/s}$, the speed in the medium is calculated as $v = \frac{c}{n} = \frac{3 	imes 10^8}{1.5} = 2 	imes 10^8 	ext{ m/s}$.

Working Principle: Refraction occurs due to the change in the speed of light when moving between media of different optical densities. The refractive index acts as a measure of how much the speed of light is reduced relative to its vacuum speed. According to the principle of conservation of energy and Maxwell's equations, light interacts with the electron clouds of the medium, creating a phase lag that results in a lower effective velocity.

Key Formulas: $n = \frac{c}{v}$ — Refractive index definition; $v = \frac{c}{n}$ — Speed in medium formula

Key Points: The refractive index of a vacuum is exactly 1.; Higher refractive index implies a denser optical medium and slower light speed.; Refractive index is a dimensionless quantity.

Advantages: Used to identify materials by their optical purity.

Disadvantages: Cannot be applied to non-transparent or opaque media.

Applications: Designing lenses for eyeglasses and cameras.; Measuring the concentration of sugar solutions using a refractometer.

Additional Info: Speed of light in vacuum is approximately $3 	imes 10^8 	ext{ m/s}$.. Option B ($4.5 	imes 10^8 	ext{ m/s}$) is incorrect as light speed cannot exceed the vacuum limit.. Option C ($1.5 	imes 10^8 	ext{ m/s}$) results from incorrectly calculating $3 \div 2$ instead of $3 \div 1.5$.

Answer: A is correct — The speed of light in the medium is $2 	imes 10^8 	ext{ m/s}$, calculated by dividing the vacuum speed by the refractive index.

Exam Tip: Always ensure your calculated speed in a medium is less than $3 	imes 10^8 	ext{ m/s}$, as nothing travels faster than light in a vacuum.

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Option B: 5 	imes 10^8 	ext{ m/s}

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Option C: 5 	imes 10^8 	ext{ m/s}

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Option D: 3 	imes 10^8 	ext{ m/s}

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