If the speed of light in air is \(3 \times 10^8 m/s\) , then the speed of light in a medium of refractive index \(3/2 \) is
Understanding the Relationship Between Speed of Light and Refractive Index
This question asks us to find the speed of light in a specific medium when we know the speed of light in air and the refractive index of that medium. The concept connecting these values is the refractive index itself.
The refractive index of a medium tells us how much the speed of light slows down when it passes through that medium compared to its speed in a vacuum (or air, which is very close to a vacuum). It's defined as the ratio of the speed of light in vacuum to the speed of light in the medium.
Formula for Refractive Index and Speed of Light
The formula that relates the speed of light and refractive index is:
\[ \mu = \frac{c}{v} \]
Where:
- \( \mu \) is the refractive index of the medium.
- \( c \) is the speed of light in vacuum (or air).
- \( v \) is the speed of light in the medium.
From this formula, we can rearrange it to find the speed of light in the medium \( v \):
\[ v = \frac{c}{\mu} \]
Applying the Given Values to Calculate Speed of Light
We are given the following information in the question:
- Speed of light in air, \( c = 3 \times 10^8 \, m/s \).
- Refractive index of the medium, \( \mu = 3/2 \).
Now, we can substitute these values into the formula for \( v \):
\[ v = \frac{3 \times 10^8 \, m/s}{3/2} \]
Step-by-Step Calculation
To divide by a fraction, we multiply by its reciprocal. The reciprocal of \( 3/2 \) is \( 2/3 \).
\[ v = (3 \times 10^8 \, m/s) \times \left(\frac{2}{3}\right) \]
Now, we can perform the multiplication:
\[ v = \frac{3 \times 10^8 \times 2}{3} \, m/s \]
The \( 3 \) in the numerator and the \( 3 \) in the denominator cancel out:
\[ v = 10^8 \times 2 \, m/s \]
So, the speed of light in the medium is:
\[ v = 2 \times 10^8 \, m/s \]
Conclusion: Speed of Light in the Medium
The calculated speed of light in the medium with a refractive index of \( 3/2 \) is \( 2 \times 10^8 \, m/s \).
| Given Information | Value |
| Speed of light in air (\( c \)) | \( 3 \times 10^8 \, m/s \) |
| Refractive index (\( \mu \)) | \( 3/2 \) |
| Calculation | Result |
| Formula: \( v = c / \mu \) | |
| Substitute values: \( v = (3 \times 10^8) / (3/2) \) | |
| Simplify: \( v = (3 \times 10^8) \times (2/3) \) | \( 2 \times 10^8 \, m/s \) |
Revision Table: Key Optics Concepts
| Concept | Definition | Formula |
| Speed of Light in Vacuum (\( c \)) | The maximum speed at which all mass-less particles and field changes propagate in free space. | Approximately \( 3 \times 10^8 \, m/s \) |
| Refractive Index (\( \mu \) or \( n \)) | A measure of how much the speed of light is reduced when passing through a medium. Ratio of speed of light in vacuum to speed of light in medium. | \( \mu = c/v \) |
| Speed of Light in a Medium (\( v \)) | The speed at which light propagates through a specific material. | \( v = c/\mu \) |
Additional Information: Factors Affecting Speed of Light
The speed of light is constant only in a vacuum. When light enters a medium like air, water, or glass, it interacts with the atoms and molecules of the medium, causing it to slow down. The denser the optical medium (generally, but not always related to physical density), the higher its refractive index, and the slower the speed of light in that medium.
The refractive index can also slightly vary with the wavelength (color) of light, a phenomenon known as dispersion, which is why prisms can split white light into a spectrum of colors.
Important Questions from Polarization by Reflection
What is the absolute refractive index of kerosene?
The refractive index of water \(_a\mu_w=\frac{4}{3}\) and refractive index of glass \(_a\mu_g=\frac{3}{2}\) . A lens placed in air has focal length 10 cm. What will be its focal length if placed inside water?
The refractive index of water and dense flint glass are 1.33 and 1.65, respectively. A ray of light travels from dense flint glass to water. The refractive index of water with respect to dense flint glass is _______ and the light ray bends _______ the normal in water.
The refractive indices of quartz crystal for right handed and left handed circularly polarized light of wavelength 762.9 nm are 1.5391 and 1.5392 respectively. The angle of rotation produced by the crystal plate of thickness 0.5 mm is:
A ray of light is incident on a transparent medium at an angle of 60°. The reflected ray of light is found to be completely polarised. Then, the refractive index of the transparent medium is nearly:
