
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
411.6k+ views
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.
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.
Recently Updated Pages
Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

What is a transformer Explain the principle construction class 12 physics CBSE

Who is Mukesh What is his dream Why does it look like class 12 english CBSE

Draw a labelled sketch of the human eye class 12 physics CBSE

What are the major means of transport Explain each class 12 social science CBSE
