Question

The absolute refractive index of Ruby is $1.7$. Find the speed of light in Ruby. The speed of light in vacuum is \[3 \times {10^8}\] m/s.

Answer 1

Hint: The ratio of the speed of light in a vacuum to the speed of light in a second medium of greater density is used to measure the Refractive Index (Index of Refraction). In descriptive text and mathematical equations, the refractive index vector is most commonly represented by the letter $n$ or $n'$.

Complete step by step answer:
The refractive index of a substance (also known as refraction index or index of refraction) is a dimensionless number that defines how quickly light passes through it in optics.
\[n = \dfrac{c}{v}\]
Where $c$ is the speed of light in vacuum and v is the phase velocity of light in the medium, it is known as Air, for example, has a refractive index of 1.333, which means light flows 1.333 times slower in water than in air. As the refractive index of a material is increased, the speed of light in the material decreases.

As light enters a material, the refractive index determines how far the direction of light is distorted, or refracted. Snell's law of refraction explains this.
Refractive Index (R.I)of Ruby = 1.7
Speed of light in Vacuum (C) = \[3 \times {10^8}\]m/s.
Speed of light in Ruby (\[{V_R}\]) = ?
\[{\text{ R}}{\text{.I}}{\text{. = }}\dfrac{{{\text{(Speed of light)}}{{\text{ }}_{{\text{Vacuum }}}}}}{{{\text{(Speed of light)}}{{\text{ }}_{{\text{Medium }}}}}}{\text{ }}\]
\[\Rightarrow R.I = \dfrac{C}{{{V_R}}}\]
\[\Rightarrow 1.7 = \dfrac{{3 \times {{10}^8}}}{{{V_R}}}\]
\[\Rightarrow {V_R} = \dfrac{{3 \times {{10}^8}}}{{1.7}}\]
\[\therefore {V_R} = 1.764 \times {10^8}\;{\text{m}}/{\text{s}}\]

Hence, the speed of light in Ruby is $1.764 \times {10^8}\;{\text{m}}/{\text{s}}$.

Note: A ruby is a gemstone that ranges in colour from pink to blood red and is a variation of the mineral corundum (aluminium oxide). Sapphires are other gem-quality variations of corundum. Ruby, along with amethyst, sapphire, emerald, and diamond, is one of the traditional cardinal jewels. The word ruby derives from the Latin word ruber, which means "red." The element chromium is responsible for a ruby's colour.