The refractive index of diamond is 2.42 what is the meaning of this statement

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the refractive index of diamond is 2.42 what is the meaning of this statement

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LectureNotes said the refractive index of diamond is 2.42 what is the meaning of this statement

Answer:

The statement “the refractive index of diamond is 2.42” refers to a measure of how much light is bent, or refracted, when it enters the diamond from another medium, typically air.

Understanding Refractive Index:

  1. Definition: The refractive index (n) of a substance is defined as the ratio of the speed of light in a vacuum (or air, which is very close) to the speed of light in that substance. Mathematically, it is expressed as:

    n = \frac{c}{v}

    where:

    • ( n ) is the refractive index,
    • ( c ) is the speed of light in a vacuum (approximately ( 3 \times 10^8 ) meters per second),
    • ( v ) is the speed of light in the substance.

  2. For Diamond: A refractive index of 2.42 means that light travels 2.42 times slower in diamond than it does in a vacuum (or air).

  3. Implications:

    • Bending of Light: When light enters the diamond from air, it slows down and bends towards the normal (the perpendicular line to the surface at the point of contact). This bending is due to the change in speed of light as it moves from one medium to another.
    • Critical Angle and Total Internal Reflection: The high refractive index of diamond also means it has a small critical angle, which leads to significant internal reflection. This property is one reason diamonds sparkle so brilliantly, as light entering the diamond is reflected multiple times within it before exiting.
    • Dispersion: Diamonds also exhibit high dispersion, meaning they can split white light into its constituent spectral colors. This is why diamonds have their characteristic “fire,” displaying flashes of various colors.

Mathematical Example:
If the speed of light in a vacuum is ( 3 \times 10^8 ) meters per second, then the speed of light in diamond ( v ) can be calculated as:

v = \frac{c}{n} = \frac{3 \times 10^8 \text{ m/s}}{2.42} \approx 1.24 \times 10^8 \text{ m/s}

Conclusion:
In summary, the refractive index of 2.42 for diamond indicates that light travels significantly slower in diamond than in air, causing substantial bending and internal reflection of light, contributing to the diamond’s brilliance and sparkle. This property is crucial for understanding the optical behavior of diamonds and their aesthetic appeal.