The cause of being the refractive index ($\mu $) of transparent medium 1, is:

Question

The cause of being the refractive index ($\mu $) of transparent medium > 1, is:

Examoogle · Accepted Answer

The correct answer is Option A: Speed of light in vacuum > speed of light in transparent medium. The refractive index ($\mu$) of a transparent medium is defined as the ratio of the speed of light in vacuum ($c$) to the speed of light in that medium ($v$). Since light slows down when traveling through any material medium compared to a vacuum, $c > v$, which mathematically results in $\mu > 1$.

Step-by-Step Solution & Concepts:
The refractive index ($\mu$) of a transparent medium is defined as the ratio of the speed of light in vacuum ($c$) to the speed of light in that medium ($v$). Since light slows down when traveling through any material medium compared to a vacuum, $c > v$, which mathematically results in $\mu > 1$.

Working Principle: Refractive index quantifies how much light is bent or slowed upon entering a medium. Because a vacuum is the medium with the highest possible speed for light ($c \approx 3 	imes 10^8 	ext{ m/s}$), any other medium possessing atoms or molecules will interact with the electromagnetic wave, causing a reduction in its phase velocity ($v$). Thus, the ratio $\mu = \frac{c}{v}$ will always yield a value greater than 1 for all common transparent materials.

Key Formulas: $\mu = \frac{c}{v}$ — definition of absolute refractive index, where $c$ is the speed of light in vacuum and $v$ is the speed in the medium.; $\mu > 1$ — the condition resulting when $c > v$.

Key Points: The refractive index is a dimensionless quantity.; For vacuum, $\mu = 1$ by definition.; For all other transparent media, $\mu > 1$ because the speed of light is lower.; A higher refractive index indicates a denser optical medium.

Applications: Designing lenses for spectacles and microscopes.; Fiber optic communication systems.

Additional Info: Light always travels at its maximum possible speed in a vacuum.. Option B is incorrect because if the speed in the medium were higher, the refractive index would be less than 1, which contradicts physical laws.. Option C is incorrect because the wavelength of light changes in a medium, but the refractive index's fundamental definition is based on the change in velocity.. Option D is incorrect because this would imply the medium is a vacuum.

Answer: A is correct — The refractive index $\mu$ is greater than 1 because the speed of light in vacuum ($c$) is always greater than the speed of light in a material medium ($v$).

Exam Tip: Remember that light frequency remains constant when passing between media, but wavelength and speed change proportionally according to $v = f\lambda$.

Examoogle · Answer

Option B: Speed of light in vacuum

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Option C: Wavelength of light gets change as it moves from denser to rarer medium

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Option D: Speed of light in vacuum = speed of light in transparent medium

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